Hello. My name is Alex and I will be happy to answer your question.
I am sorry to hear about your difficult situation.
1) The child support and custody / visitation are two completely separate legal issues and are not connected to each other, however you do have the right to file petition with the court to establish legal custody and visitation with the child, but it is not an automatic right, but rather your petition would be reviewed by the court and the court will make a decision on the child custody / visitation based on all the testimony
from you and the mother, all the facts and evidence presented and the decision would be based on what is in the best interest of the child.
2) It is difficult to precisely calculate child support payment amount, as it can vary depending on some factors, but an approximate estimate based on $10,000 gross monthly income and assuming the mother does not have any income and the mother has physical custody of the child, would be between $1,200-$1,300 per month.
You can also use official Maryland child support calculator at this link:
This is a very complex area of the law and I would strongly urge you to consult and retain local child custody attorney to represent you in the child custody and child support proceedings before the court, as these are very essential legal issues / rights, that you would not want to handle yourself without assistance of a competent local attorney.
I wish you all the best!