What the police write on your paperwork are not the actual charges. They are anticipated charges. The prosecutor charges you, the charges they file...

What can be done regarding a prosecutor lying to a judge during an arraignment hearing?

What can be done for a prosector doing their job? Nothing. They said you failed to appear, and you did fail to appear.

What would you do other than an appeal...

You can try to appeal. If you filed a notice of appeal within the very short window you had to do so.

Can you get pulled over for speeding if the cop is driving at you.

Yes you can. Radar works both ways. As does an officers estimation of speed based on his experience.

So I was caught shoplifting..

You COULD have ignored it and not payed, but now you paid, so you have agreed to it.

Can you use self defense against an officer if he tries to arrest you and tackles you for no legal reason?

Resisting an officer is a great way to get injured and charged with resisting arrest and assault on an officer. Don't do it. Courts believe police.

Will it be on my record if so Can this be removed from my record and how

Hire a a lawyer. You must appear in court. It will not be dismissed because they told you to sign.

How likely to have a surveillance video deemed inadmissible for reason it does not show guilt but likely to prejudice observers?

Very unlikely this evidence would be Inadmissible on that ground. Hire a lawyer.

If the judge made a mistake during my initial hearing regarding the citation for speeding, is it possible I could be acquitted?

34 and 39 are both above the speed limit. So, still guilty. Hire a lawyer to try to dispose of it in another manner or pay the fine.

For an out-of-state witness for the prosecution by law when are they required to give a mileage check?

I dont see a question here. If the question is "can they force me to testify and not pay me that day?" The answer is yes, yes they can.