From what I've read being put on administrative leave I cannot apply for unemployment. Because I am considered to be still employed by this company. As far as just getting a Dr's release & going back to work, yes that would be simple, however, I was dismissed or put on leave on false accusations.
You need to assume nothing. Your reading has given you incorrect information. If you are away from work for a week, on suspension, unpaid leave, or whatever, you are eligible to file for a week of unemployment benefits. It doesn't make a rats patootie whether or not you're still employed. If you are out of work (while working for this company) for more than a week without pay through no fault of your own, then you file for unemployment benefits. There is no downside to filing a claim for benefits, it does not cost you anything and there is no penalty for doing so, even if you go right back to work next week and don't ever need them.
Otherwise, they could just tell people they were on suspension forever and would NEVER have anyone draw unemployment benefits after working for them, now wouldn't they? Unemployment insurance is a federal program to provide employees with some income replacement when the employer elects, for whatever reason to put them off work without pay. It is not given out by the employers. Taxes are taken from their payroll, not your checks, to cover the payments if you qualify. A person could draw unemployment even if they were off for a two week unpaid holiday, or if the employer has a shortage of work and must put them on hold for any period of time. You do not have to be formally separated from the employer to draw benefits.
They are not only for "poor people" they are not needs based, there are no income questions, and they do not come out of the taxpayers money. Therefore there is no downside to signing up for them. In the inquiry that will be made by the unemployment office regarding your status at work, there may be some things worked out. They may decide to put you back to work. They may say you are officially terminated. Either way, they've not got you hanging out there in permanent limbo as you are now.
If you have not been dismissed for a valid, work related misconduct reason, where you had progressive discipline and an opportunity to correct your behavior and keep the job, that's not misconduct unless you did something so dreadful you should have known it was wrong even once, like setting the building on fire.
I'd file for unemployment before during and in the meantime you are dealing with all these other issues about your medical conditions. If you can't get a proper medical release to return to work, your claim may be postponed until that time comes, but you need to get it started. Then answer cbg's other questions and let her see if she can provide any useful information related to other things.