Likely #2 lithium on the lube if you choose to top it off. Thick and whiteish? Some did use gear lube, but then it went to the grease. No need to worry about overheating. Do know that the engine has no air filter though. I would run it every couple of weeks for 5 minutes or so to be sure it is ready when you need it.

The grease seems white to grey. Should I be lubricating anything else?

You my want to zip through the owners manual. A person could probably lube a lot of things I suppose. Removing the top and bottom covers and doing an inspection will tell you a lot. I also think it is a good idea to remove the drive wheels and grease or anti seize to know you can get them off in the future. No a real bad idea to get an extra belt set, or at least an auger belt for the just in case.