Classification and On-Call Compensation for an IT Worker

My question involves employment and labor law for the state of: California

I have three questions I need clarity on:

1. Do my job duties correctly classify me as an Exempt employee or non-exempt hourly employee:

I work as an Application Analyst under the IT dept at a not-for-profit hospital. I'm classified as an Exempt salaried employee. My job duties consist of providing support for onsite and remote radiologists who use a number of radiology applications to diagnose patients. I must physically be at work during my assigned shift, usually 9 hours a day or more. I make more that 48.00\hour, I supervise no one, I fix/upgrade computer hardware, software, and perform configuration changes to the applications per end user requests and Diagnostic Imaging dept management. I take orders directly from my offsite "Coordinator". Should my position be classified as non-exempt or Exempt?

2. Should I be getting paid hourly when on call, working from home and/or coming in to work:

I'm on call one week a month with a total lump sum compensation of $550.00 for the 7 days. The shift starts Friday at 5:00PM and ends the next Friday at 8:00AM. This mandatory "call" is in addition to my normal 9+ hour day shift. I must be assessable by telephone to solve any issues that may arise, by working remotely, and if unable to solve the issue remotely I must physically arrive onsite to address the issue, with no additional compensation. On average I receive 6-10 calls per night/early morning since the hospital is 24/7 operation.

3. Can I legally be on paid time off (holiday pay), and on "call" at the same time?

Thank you!

Systems analysts, etc... getting $455 or more a week are generally considered to be exempt under the federal labor laws.
Nothing seems inappropriate in the way they are paying you federal. Yes you can be on-call during time off (either vacation or holiday).
Someone with knowledge of California labor law can speak up if there are some specific California restrictions.

1.) In my opinion non-exempt. My opinion and $2 will get you a cup of coffee.

2.) If we assume non-exempt, then you need to be paid for any time actually working. You do not need to be paid simply for being on call.

3.) You CAN. The law does not say you MUST.