No, as "looking after someone" means to care for them; take care of them.
As long as you remember it you'll be fine. Prepositions don't like explaining themselves.
Yes, you could translate it as either "We looked for you" or "We were looking for you". Of course the latter would be preferred in most context on the English side, but Norwegian doesn't differentiate.
Isn't "lette" present form of the verb "å lette". Should it be "letta/letter" to have the meaning "looked/were looking" ?