Having one functioning kidney should not be a problem for BCG treatments. The BCG instillation is in the bladder and does not typically get put in the ureters or kidneys unless there is spread into those areas (rare).
I'm not sure about arthritis but I think I recall people saying they had arthritis problems related to the BCG treatments.
You are not rambling and by getting 2nd opinions early in the process you are doing the right thing. First, you want to be sure you even have bladder cancer. Then, if so, what stage and grade. Finally, the treatment options specific to that. However, you are doing the right thing by asking the questions now so you have a sense for which direction to go based on what winds up being found.
If it is bladder cancer, then grade is important to determine BCG or not also. In some cases, they use mitomycin for low grade but as long as you're getting yourself to a bladder cancer center (once all confirmed) you should be in good hands.
Hope for the best, prepare for the worst, and be happy that typically things land somewhere in between.
I wish you the best of luck!
Mike