I know it's illegal to bypass a traffic light through a private parking lot but...

No. And it does not matter that the business is operating or not.

Does paying cash bond for a friend who was arrested for not paying traffic tickets show up on my record?

The only record of your bond is with the court and the sheriff. It means nothing other than that you are on the hook for $900 if she doesn't show.

What do I do about missing this court date to move on with my life?

You can switch lawyers, and you should if you no longer want to use your current attorney. But get a lawyer. If you have a warrant the lawyer can...

How do I set a motion to dismiss my case if I don't have/hire a lawyer

You don't. It is the state's case. If you dispute it, you show up for trial and contest the matter and if you win, the case is dismissed. And if...

What did the judge explain to me?

The judge did not find you not guilty. If he found you not guilty the case would have been dismissed and that would be the end of the ordeal. ...

What do I need to do

The most you can do is to file an affidavit of non-prosecution with the district attorney's office indicating your desire to not proceed. The...

They will be on your record until you get them expunged. Hire a lawyer to file the appropriate motions.

Do I have to pay for tickets I received in the past for no license when I was 17

Yes, they don't go away. And there is no such thing as a magical clearance at age 18.

There is no prohibition on 18 and 28 year olds dating.

You can get it after you get arrested when you walk into DPS to get it. Warrants are good anywhere in the United States. Hire a lawyer and get...