2 part post:
1. If he goes bankrupt, all his assets (including his share in the house) are at risk. I assume the 70:30 split has been formalised in the title deeds. If it has not, the Official Receiver (OR) may try to claim more than 30% & this would have to be fought. He may even try to claim more if the split has been formalised, based on who has contributed to the costs - deposit, mortgage payments etc.
2. It does not matter whether a debt is secured on the house for this purpose - the assets (which include his share in the house) can be realised to pay off the creditors, whether the debts are secured or not.
3. If he has obtained credit by fraud (which it appears he did for the secured loan) his liability will not be wiped out by his bankruptcy. Did he fraudulently get this loan in joint names - i.e. did he forge her signature on the loan agreement as well as on documents to secure it? If so, you need to make sure the lender is aware of the fraud as otherwise they could chase your mother for this debt.
4. Assuming he is on the title deeds you cannot transfer the house into your name without his consent. If he does consent, the OR will look on it as a transaction at an undervalue and proceed against you to undo it.
5. If you sell the house (again, he has to agree) then the OR will want to know what happened to his share of the proceeds. If you give him 30% of the equity (i.e. sale price less mortgage and selling costs) then he will have to account to the OR for what he does with it. Your mother's share should then hopefully be safe, unless the OR succeeds in querying the 70:30 split.