Man your computer sounds pretty messed up. Even with antivirus software its still possible for those viruses to get on your machine. The best thing is to just not download shifty programs. It might be worth investing in an older crappy laptop that doesn't have any important files on it to give to the kids. Alternatively give the kid a nonadmin account with really restricted rights.
So here's the deal. You ran antivirus/malware detection and it removed a bunch of files from your computer. Antivirus/malware programs basically scan all files looking for text that is known to be bad. However, it sounds like you installed stuff which basically means you ran all the bad programs and they had free reign to do their bad things. Unfortunately, antivirus/malware detection cannot undo any of the bad things that have been done (they only try to prevent the bad things from being run in the first place by finding them early). So, you can try to put your computer back to rights on your own which I would not recommend for your skill level. I think your best bet would be to put all your important files on a flash drive and do a fresh install of windows. It seems that windows 8 also has a bunch of fancy tools that might help you fix your computer, but I don't have any experience with those and I'd still recommend a fresh install. If any of these documents are really important then I would recommend taking the computer into a specialist who can recover your files. Before doing all that and spending the money you can try a couple low risk things to get at those files. Here's what I can think to try:
1. Check permissions on your Documents folder.
- Open up a File Explorer (the folder icon)
- On the left panel you should see "This PC" and below it a folder called "Documents".
- Try expanding it, if you get an error then you should let me know what it is word for word.
- If its something about not having permissions to view it then right click the Documents folder
- Click the properties item (at the bottom) then go to the Security tab at the top.
- Click on your username in the top section.
- You should see a section with "Permissions for <username>" at the top (<username> is your username)
- You should have checkmarks in the Allow column for everything in that box. You might not have "Special Permissions" which is ok. If you don't have all the checkmarks then edit the user to have permissions. If you need instructions let me know or just google it.
2. Boot into safe mode (with networking). This basically tells windows to load without any nonessential programs running. This should block any programs your kid installed from running. Its a bit tougher to get to safemode in Windows 8 than it was in previous versions but here's a webpage that will tell you how to do it.
http://www.7tutorials.com/5-ways-boot-safe-mode-windows-8-windows-81. I believe if you boot into safe mode you have to login with an administrator account which means you should have permissions to access all your files. If you can't access the Documents folder in safe mode then you should probably call in a pro.
Good luck!