You can borrow money from 18 in the UK, so her age is not a factor.
What is a factor is that, as a student, the OP wouldn't have been able to afford all the repayments, so shouldn't have been approved for most of them, hence there's an element of irresponsible lending and/or insufficient checking on the part of the creditors and/or fraud by the mother, who may have said that the OP was working in a well paid job.
Tracing where the money was paid into might go a long way to prove that this was nothing to do with the OP. From the bank's point of view, the OP could have done this herself and made up the story about living away at university and her mother making fraudulent applications.
As to whether the DF should have noticed all the spending, he worked away for long periods, so this could be easily hidden. Sounds like he was in the oil industry, which is well paid, so their lifestyle might have appeared within their means, especially if things like jewellry was bought that he never saw. Plus the £80k could include a large amount of interest, charges and PPI, inflating the amount without any benefit to the mother.
Something to consider OP, is there any chance that your DF was financially abusive? If your mother didn't have access to money, she might have done this out of desperation, not greed. If that was the case, this would justify him paying the debt off, as he's partly responsible. Also, your mother is entitled to half the value of the marital home plus maybe pension provision if she spent a long time as a SAHP, so legally, some of your DFs assets are her's, but she doesn't have access to them, having walked away.