If non profitable organization file H1B petition, is it comes under H1B cap exemption ..?

Dear friends, I am F1 student and getting graduate in Dec/2016.

Right now under CPT I am working with a Non Profitable Organization (I’st grade to X’th grade school)

which is sponsored/funding by another Public University and my organization is ready to file H1 for me.

Can any one please answer my below questions:

If Non profit organization file H1 then is it comes under H1B cap Exempt category or general H1B category …?

What is the cap limit for H1B cap Exempt category…?, How many days the USCIS took to process petition …?

Is USCIS people accepts/process cap exempt petitions any time in year or only from April on wards…?

With this cap exempt H1B visa, do I need to stick with this employer only all the time or in future can I

change to private/profitable or another government organization …?

Friends, please answer my above questions if you know, your answers will helps me to plan my future accordingly. thanks in advance.

It will be cap-exempted as the employer is a NPO (non-profit organization)

There is no limit for this category. Processing time is 2-6 months.

It can be filed and processed anytime during the year.

You can change employers but only to another NPO. In order to move to a for-profit company, you will have to get a cap-subject H-1 which is filed in April every year.

Thank you very much Saurabh for answering my question.