For finishing I do use oil on occasion but I normally use shellac. I can get almost any look from flat (burnishing with steel wool) to very high gloss.
For the turning the base I use a friction chuck and I always have left the original center point from the very first turning.
There seems to be differences in what a person is talking about when they say they use a “jamb chuck”. The way I learned is that you take a sacrificial plate and cut a recess in it to just fit the diameter of the bowl. The bowl is then jammed into the recess. This requires making a new jamb chuck for each bowl. Except in videos I have never seen anyone use one. Many people call a “friction chuck” a "jamb chuck". Where something (either turned or the jaws of your chuck) is covered and the bowl is placed over it and the tailstock brought up. With what I call a jamb chuck, you do not use the tailstock for support. I guess cole jaws would be a scroll version of the old jamb chuck.
Jamb chuck can fit either inside or outside so when making boxes many people use one section of the box as a jamb chuck.
I STILL haven’t made one but I think a donut chuck is probably the easiest for smooth rim bowls. There are lots of plans for making a donut chuck and you only have to remove one bolt to add/remove an item.
They who can give up essential liberty to obtain a little temporary safety, deserve neither liberty nor safety. Benjamin Franklin