Can the incoming board change the budget and/or rules put in place by the developer?

The incoming board can definitely change the budget that was put together by the builder. The only restriction on that is that they have a fiduciary duty so they can’t change things arbitrarily. They have to have a good reason for doing it. If the rules that were imposed by the builder are in the CC&R’s or the Declaration, then it can be more challenging because those have to be changed by a vote of the members.