1. She is going to move to New York and look for a job after she graduates. This is fine. 2. When I walked into the room yesterday, Dad read a newspaper and listened to music. This is actually grammatically OK, but it is still the 'wrong' answer in a grammar exercise. If this were a question in an English exam, it would probably be marked as incorrect. Here's why: The sentence you have written means that you walked into the room, and AS A RESULT, your father suddenly picked up a newspaper, started to read, switched on some music and started to listen. When we have two clauses both in the past simple used with 'When', it means that the two events happened one immediately after the other - usually because the first one triggers the second. For example, it would be normal to say "When I walked into the room yesterday, Dad looked at me and laughed". In this case, it is clear that what Dad did was a reaction to your entering the room. In the case of your sentence, however, it very unlikely. The correct version of your sentence is this: "When I walked into the room yesterday, Dad was reading a newspaper and listening to music." This means that Dad started doing these things before you entered the room and may have continued doing them after you entered. The past continuous describes something ALREADY IN PROGRESS (Dad's activities) when another event occurred (you came into the room). He was already reading and listening to music, and then you walked into the room.

The first is correct. 'once' is an alternative for 'after'. 'after' is fine, but I'd tend to use 'once'. The 2nd isn't natural. If the action was already happening (father reading) then you need past continuous tense. "When I walked into the room yesterday, Dad was reading a newspaper and listening to music." If the father only commenced this reading when you entered the room, then I'd say: "When I walked into the room yesterday, Dad started to read a newspaper and listen to some music."

1. the first one seems alright 2. When I walked into the room yesterday, Dad had been reading a newspaper and listening to a music : past perfect continuous tense

The answer given by @amd16 is also grammatically OK (the only grammar error is the 'a' before music) but it is probably not the answer which the grammar exercise is looking for. There is no reason to use a past perfect here. 'Dad had been reading a newspaper and listening to music' sounds like something out of a murder mystery - for example, the son walked into the room, found his father lying murdered in his armchair with a newspaper and radio by his side. Then (when Sherlock Holmes arrived), he explained that Dad 'had been reading a newspaper and listening to music'. We use the past perfect for actions which were in progress UNTIL another event happened.