Im confused, how are trades allowed after the trade deadline?
The paperwork just has to be submitted to the league before the deadline. Then the league has to review and approve it before it becomes official. A lot of these minor deals don't get done until the very last minute, which bogs down the league's review process and explains why you see a trick of trades announced for a couple hours after the 3pm deadline.
Trades are pemitted after the trade deadline, players can also be signed; however, if the player was not on the roster before the deadline, they are not eligible to play in the playoffs.