I have a friend who (I think) deactivated his Facebook. Yet when I go on Facebook messenger it says we're friends on Facebook. Does this mean he can still view my profile whenever he wants?
If someone deactivate his/her profile (not delete), you will be friend with him/her until you remove him/her from the friend list or he/she remove you before deactivating his/her profile.
No, he can't see your profile from his profile as he has deactivated his profile but yes, he can see your public profile (whatever you have shared or will share as public audience) as normal people see who doesn't have Facebook account.
Anyone can use Messenger without having a Facebook account.