Is there any difference between leta och söka?
Not really, but they are used a bit differently. When I can't find my keys, it is 'letar'. But if I want more new friends, a partner, searching for the meaning of life, then it is 'söker'.
Is 'What are you after?' an acceptable translation?
Yes, it's a good translation imho. (The best translation of What are you after? back into Swedish might be Vad är ni ute efter? though).
No, it has to be look or search for.
That is what "What are you after" means.
Okay? We have a Swedish sentene: "Vad är du ute efter?" which I thought was more the same - but in Swedish this means more 'hidden agendas', what is Really behind your words? - not just looking for.
"What are you after?" means at least two different things in english, one of which is "What are you trying to prove?" which certainly doesn't match "What are you looking for".
Why is it letar instead of tittar
Leta means to look/search after something, while titta is just to look or watch in general.
Jag tittar på TV = I'm watching TV
Jag letar efter en tv = I'm looking for a TV
tittar can be used to say you are looking at something right?
Yes, 'Jag tittar på bilderna' (I am looking at the pictures)
How would one say "what is looking for you?". I imagined a monster or an animal when I originally mistranslated.
Vad leter efter ni?
"Ni" is the subject form, and since "you" is the object you need the object form of the word. "Vad letar efter er?" Compare "Something is looking for me" vs. "Something is looking for I".
Can it be "Vad letar ni för" ?
No, the particle 'för' changes the question, makes it into a 'questioning' of the search itself: "Why are you searching?"
Does it mean "Vad ... för" has the same meaning with "Varför"?
Yes, it seems interchangeable. 'Vad letar ni för?' = Varför letar ni? Good point! :-)
to be fair, that is an entirely acceptable way of interpreting the english sentence, "what are you looking for?"
How will you say in Swedish: what are you looking at?
Vad tittar du/ni på?
I wrote "Who looks after you ?" Obviously wrong but How would you say that in swedish ?
Vem tar hand om dig?
I wrote "what are you looking after?" is it not correct???
No. Look at my answer 4 years ago (below this one). Leta efter = looking for. When you are looking after a person, e.g. a child, someone sick, an animal, Swedish use other verbs, e.g. passa, titta till, ta hand om.