Should I worry if my baby had a bad reaction to his last chicken pox shot?

Usually NO. It depends upon what the reaction was. Fussiness, fever, or soreness are aggravating, but not overly dangerous. An anaphylactic (severe allergic) or severe neurological reaction may be the only reasons not to immunize again. Discuss with your doctor.
Depends. Most reactions would not prevent getting the second dose, but a severe life threatening reaction would make it unreasonable to repeat the vaccine.
No, Worrying not good. First of all worrying is contraindicated--that's what your health team is available for. Use the team to discuss what happened so that appropriate steps can be taken to properly evaluate the situation and make recommendations for the benefit of the baby and the parents. Secondly, if an allergic reaction to a previous vaccine or to some of the co-ingredients occurs, the series will be stopped.
Depends. There was a period after they combined the MMR with the varicella vaccine that we saw an increase if high fever reactions with the combined vaccine that wasn't seen when we gave the MMR and the v in different sites on the same day. It appeared only to affect the 1yr not the 4yr dose. I no longer offer the mmrv as a first dose to be sure. The kids still need the second dose.