How can I clean up disk space on PS4?

Check your screenshots. PS4 ALWAYS does a screenshot when you get a trophy. And that can get heavy after a while. There is also a setting (I can't remember where) where you can request your PS4 do not take an automatic screenshot when getting a Trophy.

If you have downloaded games with PSN, yes, you will always be able to redownload them with no fee. They are on your account. But there are some caviats

• As long as PSN supports PS4s you will be able to redownload them (to give you an idea, support for PS3 PSN is still not over, but for instance the Wii Virtual Shop has closed and games bought on it will no be redownloadable. So it will come at some point that you cant redownload them, but its gonna be a good while before that.)
• The game might become unlisted, which would prevent a redownload. But this is pretty rare.
• Games bought via PS+ free games will need you to keep a PS+ subscription to redownload.
• If its games you have on disk, you will be able to reinstall them via the disk as long as your disk is readable.

You didn't ask, but on PS4 the Game and its save games are separate. Check what you are deleting (if its MB its probably the save file. If its GB its the game) and if you delete the game but keep the savefile, you can reinstall the game and still have the save file. For online games (like COD) there is no savefile to speak of. Your profile is on COD servers.

I do not know of any way to archive games or zip them for later. Due to point 2, I always just delete them from the hard disk.

I would not invest in an external hard disk just for that. Really, with 1TB you must have something like 10-15 games installed at least? Pretty sure you dont regularly switch between them? Just look at the games you havent touched in a while and delete them. Anyways, like I said, you will not lose save games. You'll just have to download/install them again next time you want to play.