[Nitram Draw]

Yes, the battle map is a limited size and if the computer is controlling the battle your unarmed ships will run to a corner and die most of the time, although I have had a few rare instances where my ship was faster than the enemy and ran in circles until combat ended. It has been suggested to make the battle map larger but I don't think it is high on the list.
Basically any ship with a weapon can take out a planet given enough time. It may take 20 turns for an escort to knock out a homeorld but it can be done.
I think there was a file in the mod section that listed all the techs and the requirements to get them. It was in excel but I don't know if it is still there.
Don't know about the replay feature, as I always play tactical combat.
Hope this helps.