yes the employer can hired you back IF YOU AGREE
Generally, no, unless there is an employment contract (preferably written) with such a provision.
An employer could have a perfectly good reason for not rehiring an employee who had previously quit. Perhaps a replacement has already been hired. It would be unreasonable to fire the replacement in order to rehire the previous employee. The term discrimination is usually used in the context of some unfair exclusion of an entire group of people, the most usual case being racial discrimination. An employer might discriminate against African Americans, for example. But that would not apply in the case that you describe. If this employer did not like African Americans, then an African American would not have been hired in the first place, and therefore, would not then have been a position to quit and then ask to be hired again.
No, its your job if you want to quit then quit but no-one can force you.
The company.
assign some responsabilities to the employee
The employer will always tell you the specific reasons why you weren't hired.
No. not if you quit. For one to collect UI, they must have been laid off by the employer. The UI office will verify the information with the employer. If you voluntarily quit, you are not eligible for unemployment insurance.
Not if they're your own tools - that would be theft.
The employer can revise job duties at will - absent a union contract prohibiting that. But no employer can compel you to work. You are free to quit ans find a better deal. That is called employment at will - you are free to quit with no notice or explanation; the employer can fire you with no notice or explanation.
If your employer is asking this, and the role is what he hired you for, then you answer "yes" if you want to keep your job.
Job abandonment is when an employee has no plan on returning to the job and has not informed their employer of their decision to quit. This is known as voluntary termination.
Quit your job and find a new one.