1. You can put the house on the market, but the bank may not give you permission to sell, and you need their permission. So you should ask them.
2. I wouldn't spend the 10K. Let it be reflected in the sale price. Are you sure about the sale price? What are you basing it on.
3. Tricky question, I would always advise a sale in agreement with the bank, rather than the bank repossessing. But you are going abroad to a non EU country. Very hard to rent under those circumstances, so I think a sale now with the banks agreement would be best, that will cut down on costs, make it easier to sell, and the shortfall will not increase.
4. No the bank cannot take money from a 'possible' inheritence. You have to actually inherit before they can go after any money. Might be an idea to tell the testator to will it to your children instead, if you have children. This question is in relation to the worst case scenario.
Is the NE 50K plus the arrears of 38K making 88K. That's a sizeable amount, and think like the bank, will they pursue you or your husband. I'd say if you were somewhere like Dubai, no, UK yes. It depends.
You need to be having this discussion with your bank, and suss out what it is they are willing to take. In return for an orderly sale, they may write off the debt.
Have you thought of going bankrupt? Or one of the insolvency options.
5. So far they have not pursued your husband, and they have come to arrangments with you it appears. What did they say about pursuing your husband.