If there are savings or pensions those are marital assets too, regardless of whose name they're in. So find out all the information (search the house for paperwork, ask him etc) and see your solicitor about it. I'm sure he'd love you to walk away with nothing but it's not as simple as that.
See citizens advice bureau or debt charity about debt. When you're housed, rent comes first, debt payments after. So if you can't make debt payments they need reducing, interest frozen, bankruptcy, whatever is most appropriate. Get advice. Debts are not the priority, basic living expenses are.
Housing benefit is Local Housing Allowance, part of Universal Credit now. It's based on income not whether you work full time. Google to find out the LHA for the amount of bedrooms you're entitled to (same sex DC share, opposite sex under 10 I think share, babies share with you). Then go onto Entitled To benefits calculator, put in your hypothetical situation (income/rent/bedrooms/disability etc) to get an idea of how much LHA you'd get if any.
There's also council tax benefit. As well as a 25% reduction if there's only one adult over 18 living there.
If DC are over 18 and you're financially supporting them including housing them this may have to stop as they're legally not your dependents. They'll have to get a job and support themselves if over 18, whether by moving out or by sharing rent/food/utility/council tax payments etc with you. If over 18 they're also entitled to their own universal credit claim if their income is low.