TX debt collection law, defaulting on business loan, can creditors pursue personal assets

This will depend on the terms of the credit arrangement. Usually, small business people must personally sign for their business credit cards, and their personal assets can be levied or seized to cover the debt. Also, your other credit agreements or bank account agreements with the same institution may have provided that in the event of a default, the bank can use any asset or account you have with them to cover the debts.
Whether the bank will accept a payment for less than the minumum required by the agreement is entirely up to them.

In Texas, there are very limited circumstances in which a collector can go after your house. If you personally guaranteed the debt, they can go after personal assets, such as your bank accounts, etc. As for what to do with the collection agency, you can either hire a lawyer to negotiate a payoff, or attempt to negotiate a payoff yourself. They will often take a percentage of the original debt.