Technically you cannot apply for visitor visa for anyone. You cannot sponsor visitor visa for them. They need to apply themselves and schedule interviews.
1. should not be a problem. If she is comfortable with the misspelling using names as shown in passport is the simplest way. She can carry the voter id card as reference if questioned about mismatch.
2. your passport should not be an issue at their interview.
3. Affidavit can be prepared by your mother but do not volunteer any information not asked by VO.