With CapOne, no hard pull for you and there shouldn't be one for your cousin either.
Sorry, I just don't feel comfortable discussing cli increases about your cousin's account.
Once you've paid off your collections, it's usually about a month +/- before they're no longer on your report. You can ask the collection agency what day they report to the bureaus, it should be shortly after that.
You might see a bump in your credit score once the CapOne AU account shows up on your credit report.
if i remember correctly... If your cousin's scores drop due to high utilization, late payments, etc on the CapOne card, your scores will drop as well. You are borrowing from her credit in a sense.
Years back when i met my wife, she had zero credit history. After i added her as a AU, her scores shot right up. A few months later she was able to get her own CC (she couldn't prior).