It would appear that all the parts work together... Remember when looking at motherboards that it will have for example socket 1155. This corresponds with the CPU. (so the next generation haswell CPU's will use socket 1150 i believe and thus will not work with the current generation of motherboards)
For whether you have all the parts it would be helpful knowing what you need and maybe your budget?
For example for gaming you might want a dedicated graphics card but for general use you would not need that. Also a Z77 motherboard will support overclocking so unless you have the Intel core i5-3570k the feature won't be useful for you and you might want to look at a H77 board.
For case compatibility with a motherboard look for the word ATX if your motherboard is an ATX motherboard. This will be what your case is designed for holding. As for external parts you'll need to look at the space in the case and the size of the parts...
But as far as i can see it would all work as it is!
P.S make sure the PSU (Power supply) has enough watts for parts if you purchase a graphics card for example. This will usually state the wattage it requires and you can reference this with the wattage of your power supply.
1 - Yes they all will work together, but as ZacB pointed out, you don't need a Z77 mobo when you are going with a non-overclockable cpu. If you are not going to overclock, keep the proccy and change to B75 mobo. If you would like to overclock, you'll have to get a "K" proccy (i5 3570k)
2 - Where is the graphic card ? Also you may add a aftermarket cpu cooler if you are going to overclock
3 - I'm 99% sure that all of then are the local ones. Get a branded PSU like cx-gs series from corsair. Local case ? Well I can live with that but not local PSU
4 - It would be more helpful if you can elaborate your usage. Tbh looking at the p.s. statement i don't think that you need all that stuff
APEVIA X-TROOPER Series X-TRP-RD Black / Red Steel ATX Mid Tower Computer Case
Seagate Barracuda ST1000DM003 1TB 7200 RPM 64MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive -Bare Drive
1. will all of these work together?
2. am I missing anything?
3. I beleive the case comes with power supply and fans
4. Advise or comments?
I will be using this PC for general surfing and some gaming. I would say I am an average to light user. I am just soooo sick of over paying for garbage off the shelf.
By gaming do you want battlefield 3 ultra settings or flash games online?
If its for general gaming I might suggest going i3 with hyper threading and spend the money saved on an external graphics card. Also so you don't fry all your components a good PSU that is reliable is a recommendation... Corsare offer some very good power supply's for example.
Also you could cut the ram down to 4gb at least to start... That could subsidise a good PSU and upgrade if you really need to. Except for running virtual machines or running BF3 on ultra settings you rarely need more than 4gb