Yes you can get all the companions and skulls! Though some are quite tricky to find, keep an eye out for hidden passageways etc.
The story of the game, in short, is you play as a monstrous old god who was banished centuries ago by 5 great beings (you meet one in the demo), and has now returned to reclaim his kingdom using dark music to control the citizens.
Really glad to hear you enjoyed the game! The bridges always catch us out as well haha, they're definitely one of the hardest sections.