As to the question of grips, as you can probably tell there are many opinions on the subject, almost everyone who has posted has said something different. Personally I used non-dowel grips for about 6 months and then moved to dowel grips when I started competing and working out more hours (Level 4 /Class VI).
Your decision on grips really is up to you and your coach, if they think you don't need grips, then you don't need grips, if they think you would benefit from grips, then get them. Also the same goes for dowel/non-dowel, your coach will know.
As to the question of changing gyms... I would stay with your own gym until your coach has moved. Then after s/he has moved, go to the other gym for a "trial" practice and see which gym suits you the best. Also, waiting until your coach has moved will give you a chance to see how it will be without your original coach there, you may find you like it better. It may be that you wish to stay with your coach, or you may wish to stay with your original gym. This is one of those times in gymnastics where it's entirely up to you, no one else should make this decision for you, because it will affect you the rest of your gymnastics career. Good luck!