What should we do in order to complete our company's Stock Agreement Purchase and 83-B Form?

You should hire a business attorney and make sure you are doing everything correctly.

Can an ex parte order be enforced for months?

Without knowing more I can't say. You should speak with a local lawyer and have him or her look into it for you.

In California, what is the statue of limitations to challenge a negative employment decision by an ALJ?

You should consult with a labor lawyer in California to discuss all of your options. There may be options you are overlooking.

Hopefully you have some proof you worked during that time. You can always go back and get copies of your state and federal taxes as proof.

Should I file for unemployment as an independent contractor or as a misclassified employee?

If you thought you were misclassified why did you wait two years? Given what you wrote it is unclear what the answer should be.

Yes you need to keep them abreast of what income you have, depending on the amount.

Keep trying to contact them and find out what other documents they need.

What are my rights If my place of employment is designated an “essential” business and remains open?

You need to provide a doctors note stating your medical condition and the reasonable accommodation under FMLA that you seek (staying home).

The short answer is state but if the parties live in different states there could be other issues involved but the threshold would need to be above...

Can I hire attorney for misd. crimes before actually being charged? Most likely civil rights laws like not showing ID

You can hire and keep an attorney on retainer if you wish. I am sure many attorneys will be happy to take your money for that purpose. Good luck.