For me, my personal prayer comes before I go into the confessional as well as after. Most Catholics do what is called an examination of conscience, asking God to convict them of any sin they have done. Ususually, this leads to some heart felt I’m sorry’s before I even step into the confessional. The Our Father and Hail Mary’s are a starting point for further prayer not the ending point, for me.
As for asking Mary for assistance, the Bible tells about Christians asking other Christians to pray for them. That is all we are doing, except we don’t have to go anywhere or give any details that may be asked for. I know I can use all the prayer I can get!
And frequently, the penance I receive is to pray more for others, not specific prayers.