does claimed player count against 53 man roster limit?

What obligations does a team have to a player and the league after claiming a player off waivers? If this player puts them over the 53 man roster limit, what must the team do to get back in compliance? If the team wants to put the claimed player on their practice squad, does the player have to go through the waiver process again? Is there a timeline limit for teams resolving the status of their claimed players?