If you have a CDL, you're required to have a current and valid medical card, period.
Yes
No.
If the commercial vehicle requires a CDL to drive it, you do.
You must have a current DOT medical card to maintain an active CDL in EVERY state. That is a federal law.
It depends on what the nature of the disability is. You need to be able to obtain a DOT medical card in order to get a CDL - some disabilities will prevent this, while others will not.
Typically, two years. I believe a CDL driver over 55 must update them annually.
If it requires a CDL, then yes - that's federal law.
A medical card is required for the operation of commercial vehicles with a Gross Vehicle Weight Rating of more than 10,000 lbs. If your state requires registration of DOT medical cards, then you must do this if your job involves operating a vehicle for which a medical card must be carried by the driver, even if a CDL is not required.
To operate ANY vehicle which requires a CDL of ANY class in ALL states (this is federal law - it doesn't vary by state), the driver must have, along with the appropriate class of CDL (A, B, C), a DOT Medical Card. However, this is assuming you're were referring to a Class C CDL - several states issue a non-CDL Class C licence.
Yes you do need a CDL to be a medical transporter. Other EMT training is also mandatory.
Call medical clinics in your area and ask if they do DOT physicals.