Can I, in any way, be held accountable for any debts my Mom might have if I claim her as a dependent?

I should say that I am not a tax expert, so seeking a second opinion is good just to be sure.

No. I checked on this and you can claim someone as a dependent if they qualify under the IRS rules. You do not assume debts that they have, neither credit card nor tax debts. There are only a few cases where responsibility of debts would be assumed. Housing and supporting your unemployed brother isn't one of these, so don't worry.

I hope he is able to find a job soon. It can be a tough employment world out there.