You should be "burping" your drysuit to remove excess air. From NRS:
You want to evacuate, or “burp,” excess air from the suit. A puffy suit is cumbersome when paddling and can be dangerous if you were to get caught in a hole during a swim. One way to do this is to hold the neck gasket open with your fingers, then squat and scrunch your body, ...
Pull the leash to get the board back to you.
This is one of the safety fundamentals for paddleboards, have a leash, use the leash. When you fall off the board you pull the leash to bring the board back to you and climb on.
Actually swimming is made even more awkward by having to hold on to the paddle while doing it. Use the leash.
This will depend a lot on the fit and type of dry suit, and how much air it holds. Ideally there should not be much air inside. Too much will make it difficult to do any stroke.
You should be able to perform a basic crawl, albeit with low arms, even with some air in the suit, but if there is a lot of air, you are better off rolling onto your back and using ...
5mm wetsuits are fine for swimming in water temperatures down to around 3 or 4 Celsius. For water around freezing, you will want a dry suit if you plan to spend much time immersed.
Be aware that there are no suits suitable for those temperatures that are easy to swim in - the shoulder joints are stiffer than you would want.
Of greatest criticality in cold ...