Can I back up my iPhone on both iCloud and computer?

Sure, I’ve been doing that for years. Set up automatic iCloud backups in the iPhone settings so it backs up every day. Then whenever you do wish to backup to a computer just execute a manual backup. The first computer backup must be using a usb-lightening cable. But when it connects, you can then enable backup/sync’ing over WiFi if you wish and use WiFi to backup from then on.

To get the equivalent of an iCloud backup you will want to make an encrypted backup on the computer. And do NOT forget that encryption password (if using a Mac, the first time you make one, it should prompt you to save the password in your Keychain).

Yes.