Bankruptcy and divorce

If someone goes bankrupt post-divorce, is it the bankruptcy court that determines how much of your obligations to your ex you can afford to pay? Is it possible (due to other creditors) that you might not be required to pay any of the post-divorce obligations, at least until your financial situation improves? How do the courts monitor for financial improvements ?

Also, if I declare bankruptcy post-divorce, is it true that any property I have an interest in becomes the sole property of the title-holder (her sole name is on the title of some property we bought while married)-- hopefully an SA would be agreed to regarding the disposition of the property but I might go bankrupt before the provisions of the SA were fulfilled. Does it ever happen that a skilled spouse/attorney forces someone into this situation, i.e., property distribution is agreed to (say, liquidation/equitable distribution of proceeds), then burdensome obligations force bankruptcy, then the ex receives sole ownership of the property due to the bankruptcy of the other ex-spouse? If so, how best to avoid the situation?

No, after divorce your ex has no responsibility to pay for your obligations.

Any property that was not distributed prior to divorce has already transferred by title to the title owner, this happens automatically upon divorce.