It is a third degree felony to falsely represent yourself as an attorney to gain an economic benefit. Look at Sec. 38.122 of the Texas Penal Code. If the person pretending to be an attorney is a party to the suit or has any interest in the suit, then it seems to me they are trying to achieve an economic benefit since they obviously have an economic interest in that lawsuit. The insurance company cannot prosecute but they can bring this to the attention of the local authorities and that county's district attorney's office can prosecute.
If I understand your second question correctly, yes if one of the parties to the suit commit this crime then I'm sure it would have an impact on the civil suit. That's the kind of thing that doesn't play out very well in the civil trial and certainly it has to be taken into consideration in deciding how much the case is worth to settle. There could also be various sanctions from the court including fines and also adverse discovery rulings or exclusion of evidence.