1st, no question is a dumb question. That's what these board are for. You want to use grease. Any grease rated for marine use will work. The guys that use oil do it because they pop the seals out of the sealed bearings, turning them into a regular roller bearing set up. There are pros and cons to this. For 99% of applications, the oem standard way is fine. Also don't fill the cap completely full, because you will hydraulic the cap(no where for the air to escape to) when you try and put it on.
Grease is not needed. I've never taken apart a factory one and had much of any grease in there at all. A lot of people like them full of grease cause if its full of grease, it can't be full of water. The grease serves no other purpose since the bearings are internally greased.
Yes, the grease is only there to keep water out. So realistically 1/2 to 3/4 full is plenty. It is more important to make sure the cone o ring seals correctly, especially if you are putting the aftermarket pump cone on, as the TBM cones are more precise and a tight fit.