For patches yes you have to download the game again each time. Once the game goes to something like steam it will patch automatically. Once you download a new version of the game you can delete the old one, your saves are stored elsewhere on your computer so it shouldn’t effect them.
As for tree stumps, I’m assuming you are talking about the ones that trees you chop down leave behind. If that’s the case you can dig them up with the shovel. If you are talking about the large tree stumps scattered around the world they can’t be destroyed, although that may change at some point.