Can I get a mortgage if I already have a £10,000 loan and a late payment marker?

it would depend on: a) your income and b) how much of the £10k loan you have left to repair and c) your other commitments. However, a late payment marker will go against you.

Talk to a mortgage broker - they are the only ones who can answer this question accurately

Never happen......

Unlikely unless your income is sufficiently high.

Depends on your income and overall credit. You can repost the question with more details or just go to a bank and ask.

That depends on how much money you make, etc.