Definitely have that one rebalanced. It will be a little bit more difficult since the dot is gone but it should be better than that. Seems like the heavy side of the tire may be near the TPMS so that's what he was trying to counteract with all of the weights.
The shaking steering wheel is related to the fronts (obviously). Having them road force balanced should solve the issue.
2008 IB E92 M3| BBS | KW | Arkym | Platte Forme A.G. | Active Autowerke | K&N | Fabspeed | Dinan | Evolve-R