Miracast or DLNA (4 devices with different Specification)

3) It won't support direct casting (without a dongle), no. But if you get a dongle since your tv needs it anyway it seems, if your laptop has regular wifi, it should be able to see the dongle and transmit to it.
4) This should be as 3). As long as you have wifi support, your computer should be able to see the dongle as just another wireless device.

Now here's my 2c. Ultimately if you're not directly streaming something online and at the same time wanting to cast it to the tv, miracast is superfluous. If you have the files already there like you mention, set up DLNA and stream stuff through your local network from either your laptop or your desktop. I may be partial to this however, since both my tv and my desktop are wire connected to the router and this makes this process very easy.

If you're streaming online already on your computer, use the chrome's casting support with dongles to take advantage of this and mirror your computer screen on your tv (the resolution on this might not be great though).

Ok so I've tried this at a friend's place with chromecast. Her laptop is an older hp, at least 5 years old right now. It does not support wi-di or miracast. Her tv is smart tv and does not need a dongle. Her laptop by itself cannot cast to it since there is no miracast or wi-di support. However, she has wifi, and as soon as dongle is connected, she's able to see it and cast to it using chrome (the whole screen is mirrored). The major downside of this method is how good the wireless card is in the laptop. Hers was pretty bad so there was always like a half second lag between laptop and tv, noticeably so. Since you're not looking at the device though, but at the tv, it doesn't really matter. It will however slow down (or so it seems to me) any current stream you're doing on the laptop from the internet so it's much better if you have a file already downloaded or pre-loaded.

Same goes for the other tv that doesn't have built in smart capabilities, but with chromecast, it works just fine. And not just with laptop, also ipad, imac and even a kobo ebook can handle it just fine.
It seems to be application limited thing meaning she cannot open a netflix program on the laptop and cast from it directly but, if she goes to netflix website in chrome, and logs in, she can cast that way with no issues.

With her smart tv, her ipad and a galaxy phone can cast directly without any dongle whatsoever (they do have direct casting capability).

With all devices connected to the router, they can stream all their movies from an external hd connected to imac, to any of the devices really, as long as they have a player that supports dlna format (though setup can sometimes be a pain the first time). So this would be DLNA through the router.

I have heard the same thing about nvidia but I'm not sure what to make of it. I'm guessing it's meant for whether it can directly cast to a smart tv without a dongle of any sort the way newer phones and tablets (the more powerful ones anyway) often can. But with a dongle I don't see what difference it makes anyway.

Your dongle would go to your tv. Your tv should have a usb or hdmi port for this to work (chromecast uses hdmi). You plug it in, and find your tv from any of your wireless devices, open chrome and you'll see the little cast icon on the toolbar (https://upload.wikimedia.org/wikipedia/commons/thumb/2/26/Chromecast_cast_button_icon.svg/1280px-Chromecast_cast_button_icon.svg.png). Press it and you should be good to go.

It should be said, I have not done this extensive a testing with many dongles. Read up in advance what applications will work with the particular brand you're buying, and what the limitations are.

Looks like http://any-cast.com/user-tips.html it should be able to do it but support for it (or lack of it) will depend on windows, not on nvidia. Or that is what I'm understanding from that guide anyway. Instead of built in cast icon into chrome, you open any browser and use the anycast's IP address.

I don't know enough to recommend one over the other. I've tried appletv and roku but not the stick you mention so I can't tell you buy one over the other. In theory, there is no reason why the one you want to use won't work. It's not anything special on the part of google tech that makes it work. They just own the browser so have the compatibility built in instead of you having to do few steps of your own.
But I don't know that that's worth extra $32.

Ok do you have a way of buying this in a brick and mortar store, instead of online? Because then you can take it home, try to make it work, and if it doesn't just go and return it. Online shipping makes this largely not worth it.