To address your last question first–at least from the text of the constitution, it looks like there is no distinction between a veto made when congress is or is not in session-- so I would think that, as long as what the prez does is veto a bill, that veto can be overridden.
A pocket veto is the only way the president can avoid a veto override (At least temporarily–congress can always re-pass the bill, and get it to him at a time when he can’t pocket veto it).
The answer to all your other questions seems to me to be politics–in your first case, refusing to sign a bill is a gesture, and appearances matter-- the president may want a bill to pass, but also be able to legitimately argue he’s against it, or at least does not support it–and hence may choose to not sign a bill (knowing it will become law), for the effect as a gesture. (just like a senator voting for cloture, knowing that the majority supports the bill–so it will pass–but then voting against the bill itself (so he can claim he opposed it). Similarly, a veto override probably makes the president look weak–so he may not want to veto a bill he opposes if it will clearly be overridden–if it is inevitable that the bill becomes law.
Similarly, in your second case, a veto is a dramatic act----whereas a pocket veto is a little-known procedural trick. So, if congress isn’t in session, he may prefer to use the pocket veto on a bill he doesn’t like, so that its failure to become law is less dramatic or noticeable. On the other hand, if popular opinion is against a bill, the President may want to veto rather than pocket veto–to get his opposition to the bill clearly on the record.