Do not be afraid. If you can, consult with a criminal defense attorney who can appear for you. If not, your tickets are administrative in nature and I would not generally see someone in your position be arrested. The fact that you appear in person voluntarily will hold you in good stead.
This non-Texas lawyer has given you terrible advice. His advice might be true in California, but it's worthless here. These are not "administrative" tickets in Texas; they are Class C criminal offenses and if they have warrants attached to them, then you could be arrested on any of them. Call the court to ask them what their policy is on arresting people who come to the court to try to make payment arrangements. Almost all of the time they will not try to arrest you. Keep in mind that by paying the no insurance ticket, your license will be suspended.
I would recommend contacting a local lawyer that handles Class C offenses. He or she may be to help you lift the warrants and minimize the number of tickets you have to plead to (especially the no insurance ticket).
Since you have warrants for your arrest, I would advise you to contact a local attorney to help you remove the warrants and then take care of the tickets. Good luck and God bless you.