After all research is "owned" by players. Do I need to keep the Patent Lab? Or can I just use the space for something else -- while keeping all researched benefits?
No, you can destroy it after you've acquired all the patents you wanted. They won't be lost. Additionally, you may even mutiny another player's patent lab and do research in the limited 120s time period. Once it's over, the control over the lab goes back to the original owner, and you get to keep your patents, even if you never had your own patent lab.