Does Asus Radeon HD 7970 3GB take 3 PCI slots?

The rear view picture on Newegg is pretty clear - Yes, the Asus card takes 3 slots.

The one you listed almost certainly uses 3 slots.

a) It still connects via only one PCI Express 3.0 x16 slot, but takes the space of 3?

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Yes.

b) Would I still be able to fit a wirelles network card and maybe a sound card in the case?

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I don't know.

c) Doesn't seem to have a HDMI port so if I want to connect it to a plasma TV do I need one of these DVI to HDMI cables?
http://www.amazon.com/BlueRigger-High-Speed-Adapter-Cable/dp/B005LJQP0E/ref=sr_1_13?ie=UTF8&qid=1365961814&sr=8-13&keywords=dvi+to+hdmi

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It also has a ton of displayports so you might be able use one of these too: http://www.amazon.com/Startech-DP2HDMI-DisplayPort-Adapter-Converter/dp/B0017K6BDW

b) Would I still be able to fit a wirelles network card and maybe a sound card in the case?

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not both.. you can use the top most pci-e 1x port to add either a network card or the sound card as both types use pci-e 1x slots .. your other 1x slots will be covered by the gpu

The Asus card you have picked comes with a DVI to HDMI adapter. Out of the box it provides an HDMI solution.

I would however recommend a GHZ edition card instead, as the price difference seems to be about what you were willing to pay for the DVI-HDMI cable (before the rebate.) I would consider the slight bump in price worth the performance gain. Here's one with a better rating, a 2-slot design versus 3, native HDMI, and it appears to be in stock:

http://www.newegg.com/Product/Product.aspx?Item=N82E16814125439

The motherboard you have selected will accommodate plenty of add-in cards, even if you go with the three slot Asus card. You would still have room for 4 more cards.

I would ditch the Encore sound card from your build. It's based on a VIA chipset, just as the motherboard's built-in sound is, but the motherboard has a newer chipset, so you really wouldn't be gaining anything by going that route.

In case you are still concerned, you have many options for a wireless adapter. PCI, PCI-e, or USB. Because of the speed of wireless networks, any interface solution should work transparently to you, however the adapter you choose could impact performance based on the antennae it is equipped with. You can use any of the PCI-e slots for a PCI-e wireless adapter, it doesn't have to be a x1 slot. In fact, only the top x16 slot has all 16 lines going to it. The 2nd has only 8 3.0 lines, and the bottom has only 4 PCI-e 2.0 lanes. If you are concerned with using up your PCI-e slots, just get a PCI card. PCI is more than fast enough to accommodate wireless.

I use asus xonar DS the cheaper one and its a heck of a good deal for a sound card and sounds great on good speakers too.
http://pcpartpicker.com/part/asus-sound-card-xonards

Also i'd ditch the wireless card if you want to save some space in the case and just grab a usb wireless stick I haven't had any issues with them before just plug and play with the cd.

I have the worst issues with drivers on USB wireless sticks. I would rethink.

I would go with on-board sound for now. Frankly, since Windows Vista, the advantages of extravagant ad-in sound cards has been mostly mitigated, as all of the sound "work" is handled through the operating system, not the sound card. All you're paying for now are mostly better amplifier circuits, some different connector choices, and questionable driver software. On-board sound has come a long way in terms of signal-to-noise ratio, so the difference in quality isn't as noticeable anymore between on-board or ad-in cards, especially when you don't have a good sound system to listen through. I'll recommend again that you start with the on-board, and if you find it doesn't serve your needs, you can always turn it off, then add in something else.

What you choose is also dependent on your final destination for your sound. If you're doing a home theater type computer, and plan to run your audio to an external amplifier with surround speakers of some fashion, you would benefit from a sound card that comes with "Dolby Digital Live" or "DTS Connect" for encoding types, and some sort of digital connector, either S/PDIF or coax, which you'll find as either a phono plug or something that looks like a headphone jack. Doesn't really matter which you pick, as they all carry the same digital bits. If however, like many computer users, you just plug in a simple set of stereo speakers or headphones, definitely do not spend extra money on these things. You won't hear the difference. The encoding is important when playing games that support surround speaker configurations, and up mixing music into surround, but when watching movies such as DVD or Blu-ray, you actually don't want encoding done by your computer if you can help it, and rather should allow the pre-encoded soundtrack to pass through to an external decoder, to preserve quality.

Your HDMI cable will be fine.

On another note, if you are outputting audio over your HDMI cable to your plasma screen, you will be using the HD audio on your graphics card. It wouldn't even use an ad-in audio card if you had one, in this case.

Some advantages of a sound card are:
More inputs/outputs
Potentially higher output power
192 khz sampling in many cases
32 bit samples at high same rates
Lower noise floor

But in most cases the onboard sound works just fine.

The specs for the sound on the GA-Z77X-UD3H are not bad. It's using a modern codec, the VT2021 which supports Dolby Home Theater and DTS Connect, and they have a shopping list of other supported formats, so there really is little need for an additional sound card. Is there a reason why a person would need higher output power from a sound card, unless powering multiple headphones or using unpowered speakers?

•Intel High Definition Audio Specification Rev.1.0 Compliant
•Exceeds Microsoft Windows Logo Program (WLP) Requirements
•High-performance ADCs with 100dB SNR, DACs with 110dB SNR Various Output Format
•5 Stereo DACs Output Pairs supporting 16/20/24-bit, 48/96/192/44.1/88.2 kHz sample rate
•2 Stereo ADCs supporting 16/20/24-bit, 44.1K/48K/96K/192KHz sample rate
•2 independent 16/20/24-bit S/PDIF TX Outputs supporting 48K/96K/44.1K/88.2 KHz sample rate
•Content protection for full-rate lossless DVD audio, Blu-ray DVD, and HD DVD audio content playback*

You're likely to get as many answers to the thermal paste question as the number of people you ask. I really doubt you'll get your $12.99 worth from your thermal paste. At best, you'll likely never get more than a few degrees difference from the best thermal compound to the worst, and that's provided you apply it correctly. Also, unless you attach a lot of heat sinks, you really don't go through it. If you check out the last photograph on Newegg, of the CPU cooler you have selected, it just happens to come with a tube of thermal compound already. You can save the 13 dollars right there, or recycle it toward a better cooling solution (which you don't really need) or even one of your other components. What I'm trying to say is, a more effective cooler will give you more return than buying the fancy thermal interface material. Also, the processor you have selected comes with a cooler already. It shouldn't be necessary to upgrade the stock heat sink / fan that comes with your processor unless you plan to overclock or run it in an excessively warm climate.

The gripes concerning Windows 8 are mostly opinions, not facts. If you approach Windows 8 with a positive attitude and open mind, you will learn that it can be more efficient than Windows 7, and folks running Windows 8 on a laptop enjoy longer battery life. I've been using both 7 & 8 since release, and 8 makes me feel toward 7, how 7 made me feel toward Vista. It can take some time for the subtleties to sink in, but that's where you can really appreciate the improvements. Something as simple as wireless network management, for example. I changed the password on the Wi-Fi at the house the other day and, with my Windows 8 machine I simply right clicked the wireless network and then clicked "Forget this network," and proceeded to log back into it. With Windows 7 you have to go into the properties for the wireless network to change the password, which is a more cumbersome and less intuitive method.

I program as a hobby, but nothing too professional. I think you'll enjoy the whole project, and once you get Windows 8 up, the fun of exploration begins again.

I will just warn you the interface is extremely unintuitive.

A touch screen is preferred but not required and it is alittle buggy. Not slow though.

Note that I do not have W8 on any computer. I have used it in stores at at someones house though,

See, now we're already blurring the lines between opinion and reality again. I wouldn't say it requires touch, or even that a touch screen would be preferred. Slow or buggy is not the case either, although those are highly subjective. I wouldn't mind having you quantify what you mean by "alittle buggy," smeezekitty.

It's running on an updated kernel, so is faster and more efficient, and has larger buttons, if you prefer using the "Start" interface to launch your applications.

For those who say the start button is gone, I ask you what happens when you place the mouse in the lower left corner of the screen? A big "Start" appears, and clicking that is what gives you the Metro interface, which is nothing more than a full-screened version of the Start menu, with "live tiles" as they put it. It's more functional by far than the older Start menu, and as it's been said before, when using the start menu, I never found myself much interested in everything else that was happening on the desktop.

I doubt it is possible to get completely unbiased data from any forum member.

When I said "alittle buggy", I found the start interface quirky and it tends to jump around a bit. Nothing major really.

I found it was atleast as fast as W7 on comparable HW and from what I have heard shutdown/startup speed is improved.