A: If she is unwilling to sign a power of attorney document, you will need to take up an adult guardianship lawsuit. Connecticut appears to have adopted the Uniform Power of Attorney Act, which typically will simplify what is required to draft a power of attorney document. An attorney should be able to do that for you cheaply here on Contracts Counsel. However, if your mother will not voluntarily sign a power of attorney document, then you will have to try to obtain a guardianship. I should mention that the uniform power of attorney document may not allow medical decision making, so you may need a more complicated document. Either way, you will need to speak to an attorney licensed in your jurisdiction.
A: Courts will protect you from an illegal deal, but they will not protect you from an unwise deal. On its face, this is enforceable. However, I know Texas has some very strong consumer protection laws and a Texas attorney may be able to help you with that. You will need to speak directly to a Texas attorney. I'm in a neighboring state and not licensed there.
A: The rules for the salary basis of pay is governed by a federal law called the Fair Labor Standards Act. It allow an employer to deduct an entire day's pay if an entire day of work is missed. If any part of such a day was worked at all, then a full day's pay is required by law. HOWEVER, there is an exception under which partial day deductions for partial day absences is allowed if an only if the absence is for Family and Medical Leave Act leave. I'm not licensed to practice law in Texas: if there is any peculiar spin on it through state law, perhaps a Texas attorney will chime in.
It is ordinary for an employer to substitute PTO for salary pay when a whole day is missed.
A: 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.