You won't hurt anything by
trying to install 3rd party apps in a user's home folder. As previously recommended, it's a very good idea to name it "Applications" and directly in the home folder, not in Documents or anything else.
Also as stated, some 3rd party apps just won't be happy there, and will only run (or only run reliably) in the system-level Applications folder. Not much you can do about that.
It's not clear if you want to segregate any Apple apps this way. Apple strongly discourages this. Some may work if moved out of the system-level Applications folder, but others either won't work or will do any number of bizarre things. Also, if you ever upgrade or reload your system, you can end up with 2 possibly-different versions of the same app, perhaps with their support files mixed, overwritten, or otherwise corrupted. Many rather nasty possibilities.