This is for Canada, but I'm pretty sure the same would apply in the US. The short answer is no, because most employers will have an exclusivity clause in your contract that means you cannot work for another employer while you are with them, and you are still under contract while you are on disability.
You can probably quit your job while on disability and not be adversely affected, but I would definitely suggest reading your contract before doing this to make sure your employer won't be trying to recoup the disability payments. You might also find that your employer would terminate your disability if you gave notice, although I'm not sure of the legal background to this (employment law is very vague in Canada).
Yes, he could do that.
As far as I know, when you are on disability your are to return to your employer with either the same or similar position. They can give away your position, but you are allowed back onto the job with a similar or same position. For example, you stock shelves in a store in Dept A. making $$ an hour. You go on disability and they put another person in your spot. When you return to work after being on disability your employer is obligated to have you stock shelves as before at $$ per hour, but it may be in a Dept B. I hope that makes sense. I would fill out the FMLA form because that protects you.
It really depends on the employer and their educational requirement for that position. Each employer may have a different requirement.
After the note has been signed and approved, you don't have a whole lot of leverage. It may be too late to do anything about it - but - it wopuldn't hurt to talk to the lender and ask that certain facts not be disclosed to your employer.
what position did you hold at your previous employer
No.
It depends on the employee, the employer, the industry, and the type of position.
You dates of employment and what position you held.
In Canada the Employer can give your position to someone else for the time you are away, but must give you that position back when you return. However, if you are on and off Worker's Compensation then your Employer has a right to give you another position which you can handle with the condition you have. An Employer cannot fire an Employee that is on Workers Compensation.
what are an employees rights when returning to work after fmla and full time position is nolonger available, but lower paying part time position is in a different department?
Yes.
No, you always have the option of quitting (and it would probably be considered involuntary termination for unemployment purposes). But, can an employer decide your precise job responsibilities are no longer needed, and instead offer you a different position that you don't like (or even physically cannot do)? Almost certainly, unless there's something in your employment agreement that explicitly forbids it.