If you don't get custody, you will very likely have to pay child support absent certain circumstances like 50/50 possession and access or a grossly disproportionate earning on the part of the custodial parent.
The affidavit of support in Texas has really only been construed to be a contract-- if she doesn't support you, you can sue her for breach of contract but that's about it.
I'd recommend consulting a local attorney.
Adultery may have an impact on your divorce (the division of community property), but in most cases that is a very small issue. It has little or no impact on what happens with custody or child support.
No, your wife's grandmother has no obligation to support you or to pay your child support. Those are your responsibilities.
I recommend focusing on improving your employment situation. Your support obligation will be based on a percentage of your income (20% of your net available resources). The more you make, the better able you will be be to support yourself and your child.