Is it legal to termiate an employee who refuses to relieve their Supervisor without monetary compensation

Yes, but they are probably entitled to unemployment benefits for losing their jobs.

Can an employer tell me that I can't work from home unless there is another person at home with my child, ie spouse, nanny, etc?

It sounds like the rule applies to both men and women with children at home. If so, it would not be discriminatory.

At my job they are moving me to a different office which is smaller and closed doors and I'm claustrophobic. Can I sue them?

You could ask them for an alternative arrangement because of your medical condition. They may ask for a doctor's note to confirm your disability....

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My DON said if I keep using my FMLA I will be transferred to a different shift .

You could have your doctor write a note stating specifically which duties on the day shift you can do and which you cannot do.They will have to...

What can I do if I was wrongfully suspended

Unless you have a union, I don't think there is anything you can do except refuse to return to work and apply for unemployment benefits.

An old co worker sexually harrassed me by saying he wants to F$&@ me and will pay me if he has to. He poured Hennessy on me and

This seems more like a matter for the police than a private lawsuit.

You could have called the police, especially if any of the shouting involved violent threats.

Worked in healthcare

If your annual evaluations were good, and you were not given a warning, then you most probably will be awarded unemployment benefits.

Fired from my job am I entiled. To all of my vacation Time

You should be entitled to your vacation, pro rated. For example if you have 2 weeks per year, and the year starts in January, you should be paid...

Is this sexual harassment and can I sue company for compensation?

If the sexting is upsetting to you, you need to consult with an employment lawyer to discuss your options and their implications, including what...