I used an estimate of 45 billion lightyears, from memory, apparently slightly out of date. Apologies.
It is fine. The answer does depend on assumptions about the size of the universe anyways, as it is always possible that the actual universe is smaller than that are what is seen on the edge has circumnavigated the universe before.
Anyways, any question of exploring the universe depends on the size of the universe. Currently there is no reason to assume that the observable universe is equivalent to the size of the universe. If you just restrict it to a single galaxy, then in the lifetime of the universe exploring a galaxy is technically possible, even if it is difficult.
As for the impact of the expanding universe on the entropy of the universe, that is not something that I am familiar with. I have not dealt with cosmological aspects of anything in my research, so I am not qualified to talk about it, which trying to find some papers about it.