Unfortunately, the answers to pretty much all your questions is... We don't know!
Why isn't Thor looking for Odin?
Does it mean he hasn't found out about Loki posing as Odin?
In fact, Loki was originally intended to be in Age of Ultron and still on the throne. The scene was cut as it confused test audiences who thought Loki was controlling Ultron.
The cut scene is not available online (AFAICT) but Jos Whedon told various sources
"We even had a little reference to the fact that he’s taken the throne, which was Tom doing his Anthony Hopkins impression when Thor says, 'Oh, what would father say?' Then Tom does his Hopkins impression, and Thor’s like, 'That is uncanny!' It’s sort of like his subconscious is telling him that Loki was imitating his father. But he would never make that connection."
Source - CinemaBlend
Full answer over on our sister SE site - Science Fiction and Fantasy
In Doctor Strange Thor comes with Loki in search of Odin, this means that he found out about Loki after Age of Ultron.
What was Loki doing till then?
What was he doing? Ruling Asgard it is presumed but it seems likely that the deception has now been discovered since Thor is now looking for someone (Odin) that he didn't know was missing before...but we haven't seen the discovery.
The only reference is the post-credit scene in Doctor Strange and is described by Thor as
"It's a bit of a long story. Family drama..that kind of thing."
If Thor believed that Loki was dead during Avengers 2 wouldn't he have told the others about it?
You know, I thought he made a passing reference but I can't find it in the transcript but it does seem odd that the subject didn't come up.
However, Thor tells Erik Selvig and other people that Loki is dead in The Dark World so perhaps he assumes that the Avengers already know. Recall that some time has passed between TDW and AOU, Thor is in action with the Avengers. Perhaps he's already had that conversation.