Etter, til, for. ....... Interchangeable??
No. They're used differently in different contexts.
Can 'etter' mean 'after' in this context?
No, as "looking after someone" means to care for them; take care of them.
How would you say that? (Please)
What would "We looked after you" be?
I am using "etter" now here, but do not know why
As long as you remember it you'll be fine. Prepositions don't like explaining themselves.
Question about the past tense. This form of the past tense is truly both the simple past and the past progressive?
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" ?
"Lette" is both the infinitive of "å lette", and the past of "å lete".
The past tense of "å lette" is "lettet" or "letta", while "letter" is the present tense.
So "så på" is "looked at" and "lette etter" is "looked for"?