congrats for giving it a shot Terry, you should be proud of yourself. Looking at the cutter above, I'd suggest creating some clearance on both sides of the cutting edge, not just on the front side or it will rub. Also, make the cutting edge narrower and do more than one plunge cut to get the groove width you want. think of this as an internal parting tool - too wide and it'll chatter.
For the getting it on center problem, you can either make the grooving part shorter, if it's much longer than the depth you need. Or grind a similar tool from an old endmill or piece of round HSS and rotate the cutter, so that it's more of a negative rake.
I'm guessing that you have the work as far into the chuck as you can or supported by a steady?