Is it possible to download iOS apps on a PC, then transfer them to my iPhone?

If so, how would I do this?

Not possible. The apps have to be authenticated on your iphone

It is possible but you need a specific version of iTunes to do this. Apple a couple of years ago removed the App Store from iTunes but they did release another version for people who still want it.

You can get that version of iTunes here -

Note: You won't receive new iTunes updates if you install that version.