It's possible they are related.

Big transaction, running on slow disk, and getting deadlocked.

The IO errors could also be due to the wait for the transaction log to grow.

Hard to say without knowing what the queries are that were involved in all three errors/warnings that you displayed.

The deadlocks could be related to slow IO. They could be related to bad indexes. They most probably are related to bad queries (which could cause tempdb log use, could cause slow IO etc etc).

Find the queries involved in those errors, and then evaluate them to determine the causality of the errors.