I don't know how many programs will fit inside a folder in the default Android OS, or the default G4 Launcher, but I'm going to say with relative confidence, at least as many icons as will fit on your screen. I use Nova Prime as my launcher, and while I don't know what its maximum limit is, I do know that it will hold more than a screen full of icons, and allow you to scroll through the open folder to see the additional icons.
Now for the (possibly) bad news. Miracast, does not work well for me on the LG G4, but to be fair, it also doesn't work well for me on most systems. For a wireless video system that is 2 years old, it is a remarkably unreliable system (in my experience). My ($5000, 80 inch) TV natively supports Miracast, and while it did work with my Turbo, it did not with my Surface Pro 3, nor my G4. I also have a Rocketfish solution that also worked for my Turbo in my home theater receiver, but not my G4 and also not my Surface Pro 3. To be fair, I haven't found anything that works on my SP3 (although maybe Windows 10 fixed this -- anything is possible).
If you happen to have a Roku, you can use it to display photos from your phone, but I don't know about video.