What can I do as a Teacher if employer won’t give me my hiring agreement in writing.

Good morning, Florida is an "at-will" state (with a few limited exceptions). Depending on the size of the employer, you may be subject to FMLA protections. Otherwise, unless there is an employment contract in place, an employee can quit at any time and an employer can fire an employee at any time. Unless the reason for the firing is illegal, such as a protected class or whistleblower protection, you can be fired while on sick leave.

Have you asked about receiving the promised bonus? It may just be late. I would talk to the employer before quitting. And, yes, you must still give the 30 days' notice or you will be in breach. Also, realize, if you quit you may not be entitled to the bonus. I would have to see the contract you signed to actually know what you are entitled to or not.

I would have to see the employment agreement/contract. Also, if you have a job description with duties, responsibilities, in-office/hybrid/WFH requirements, reporting requirements, etc that would help.

No, it's not. California has a very strict law against non-competes, and views those as illegal restraints on trade. Pretty much the only scenario in which a non-compete will be enforceable in California is in connection with the sale of a business.

You will need to talk to someone in California, specifically. I am not licensed in your state. Generally, it is possible for terms of an agreement to service termination of other aspects of the agreement. This comes up in employment contracts all the time. The answer to your question most likely exists in the text of your agreement. Take that to a local attorney - aside from the text in the document, there may well be case law in California that would set an upper limit on how long such restrictions can last.