Papyrus wants to be apart of the royal guard but undyne doesn't believe he has it in him but still helps by giving him training.
He wants to catch a human so he can prove to Undyne that he should be apart of the royal guard.
He is unaware of the fact that he was once Gaster. He believes that he and Sans are brothers and enjoys living with him but can't stand his puns.
He loves puzzles and collecting things.
He is a big kid, he loves action figures and being on the undernet.
He loves to make puzzles and cooking.
he always excited about everything he will do anything for friendship.
He loves bed time stories and watching Mettaton.
When upset or if memories of his real self happens he glitches if it happens very badly it can turn him back into Gaster.
He believes that Sans is his brother. They live together and enjoy each other's company but Papyrus really hates his puns.
He didn't really get the chance to get to know Sean.
He is unaware of the run away Queen
He wants to impress her so he can be in the Royal Guard officially.
If you check his computer in his room it is hinted at that he and Alphys knows each other on the internet as some of their emails are on his desktop.
He is unaware of Gaster's existence let alone he himself being Gaster it is as if his memories were erased or rewritten.