"He continues to keep her on his health insurance plan since she is attending college full time."
"Her" meaning a daughter? Remember, we're strangers and random use of pronouns without identifying who you're talking about can be confusing.
"My first question is this mandatory on his part."
Regardless of whom you're referring to, unless it's in the divorce decree or incorporated settlement agreement, no, it wouldn't be required.
"Is he requred by law to keep her on his insurance plan and is he still required to pay half of her medical bills since she is over the age of 18."
Refer to previous answer.
"The other issue is we continually get harrassinig phone calls, voicemails, and other phone messages from his ex-wife threatening to take him back to court for more child support, but she has not done it."
He's free to take up the harassment issue with local law enforcement or, failing that route, via the divorce court or a civil harassment suit.
"He also signed an agreement in the divorce decree to pay 50% of college expenses although he was supposed to be involved in the decision making process this has not occured."
If the agreement says he's to be involved in the decision-making process, he's free to take the issue back to divorce court on an enforcement-contempt motion and ask the court to also order her to pay his legal fees.
"She said she would not live with us and that she would live in a dorm. I know it is not Texas Law to require him to pay college expenses but what are our options when she refuses to live with us instead of paying dorm expenses."
What does the decree say? Does it not define "expenses"? If it doesn't, he's free to ask the divorce court to clarify the issue.
It all boils down to what the decree-marital settlement says and, if it's not clear, whether he wants to spend the money to get clarification from the court.
He should be talking with his divorce attorney; if he didn't bother to have one, this may or may not be chalked up to that fact.
"There is no reasoning with this woman and we are tired of the threats and harrasement."
You might want to change your phone number if there's no harassment angle to pursue with cops and you don't want to spend money on a civil harassment action.
"We have been asking her for years to send us copies of original medical receipts but she refuses."
I trust you have done this "asking" *in writing*.
"Is he requred to pay for this childs medical."
Whether the child is now 19 is irrelevant. If the decree has him liable for X amount of unreimbursed medical expenses, he should pay it if it's a bona fide receipt.
"Can someone please help us resolve these issues so that we can live a normal peaceful life?"
Your husband needs to talk with his-a local family law attorney, among other things.