If I delete a game I downloaded, can I reinstall it later?

You will get to keep your games. You'll notice that when you get the free PS+ titles, they're added to your account whether you download them or not. Uninstalling games will not remove them from your library, which can be viewed at the far right of the PS4 home screen.

i.e. the library is tied to your PSN account, not the console's hard drive.

Please note that should you cancel your PS+ subscription at any point, any of the free monthly games you have in your account will be removed from your account until you re-subscribe to PS+.

Normally, you can download any game you've downloaded before as often as you want to, free of any additional charge.

However, there is one exception to that rule: If the game has ever been pulled out for any reason, you won't be able to download it again until it somehow returns to the PSN. Luckily, the list of games that have been removed entirely is very short (the latest example would be P.T., which is a demo), and you can still use the game until you decide to delete it.

As for PS Plus games, they're treated like any other game. Just keep in mind that you won't be able to play those games without a valid PS Plus subscription. If it runs out, you only need to subscribe again in order to play.