1. Yes - as things stand - the house is at risk if he goes bankrupt. This does not mean there is 100% certainty it would be taken, but it is pretty likely that would be the outcome after a period of time (probably at least 12 months after be became bankrupt).
2. If you are in a position to make a bigger offer & pay the money then it might be a good idea if it does result in him avoiding bankruptcy. Note that unless you trust him 100% it would be better if you paid the money direct to his creditors & not to him. Also note that the mortgage lender will only agree to his name coming off the mortgage if they are satisfied that you alone have sufficient income to keep it up to date. However, this all sounds quite complex & you really should have advice from a family law solicitor.
3. Immediately he is bankrupted the Official Receiver takes an interest in his assets, which include his share of the equity in the house. As a result, I do not think he would be able (or the Court would be able to order him) to hand over his equity share to you. So it is very important to get the divorce financial settlement implemented before he goes bankrupt.