Transformer installation

My house has a 16V 10VA transformer for the doorbell. I bought a 16V 30VA transformer, and tried to install it. Easy? Simple? The 10VA transformer is attached through a knockout on the side of the breaker box. The 16V wires are attached to the outside, while the high voltage wires are threaded through the knockout hole. However: * The three high voltage wires are connected directly, without any wiring nuts, to the breaker and the ground bar. * The green wire and one of the black wires are attached to the ground bar, and I **can't** loosen the screws that hold them to the ground bar. If I can't loosen the ground bar screws, I will have to cut and strip the existing wires, and use a wiring nut to connect the new transformer wires to the existing wires. * The other black wire is attached to a 15A breaker. Questions: 1. Why is the existing 10VA transformer double grounded (ground and one side connected to the ground bar)? 2. Is it OK to attach a 30VA transformer to a 15A breaker? The circuit only powers the chime solenoid and the video doorbell. They say 10VA is not enough for both, but will they pop a 15A breaker? 3. I only have small wiring nuts. Will I need to buy larger wiring nuts for the larger gauge wires?