Is it permissible to work for a company whose owner mixes gambling money with business money, and is it permissible for him to pay his debts through gambling?

There is no harm in working for the company as long as the work itself is permissible. The mixing of unlawful wealth with lawful wealth does not affect its permissibility, because the unlawfulness of wealth pertains to the liability of its owner, not to the specific currency itself. As for the company owner betting on horse races, if it is merely predictions, then this is prohibited gambling. However, if he is betting on his own horses, there are specific regulations governing its permissibility for him.