Is it possible to transfer my H1-B visa to another company if I get a new job

You need to speak with a lawyer about the specifics of your situation - I can provide only general guidance as yo your questions.

a) Officially, if you are terminated, there is legally no "grace period" - once you cease working for the sponsoring U.S. H-1B employer, you are technically no longer in H-1B status even if the termination is through no fault of your own.

However, when seeking to transfer an H-1B to a new employer while here in the U.S., USCIS will want to see documentation of maintenance of H-1B status in the form of as pay statement from the original H-1B employer which is dated within the 30 days before filing. If a petition is filed to transfer the H-1B to a new employer within 30 days of the date of the last normal pay statement, USCIS will generally accept this as evidence of maintenance of valid status. This is not a "grace period" legally speaking, but may have the effect of one.

Of course, if you apply to change companies before termination, there is no issue - and if you HAVE been terminated and do not have a pay statement dated within the last 30 days before a new-employer petition is filed you can simply leave the U.S. and reenter on the new H-1B to return to valid H-1B status (but her eit is especially important to speak with a lawyer about the timing of your departure).

b) There is no specific requirement as to the company/type of business, other than that it be offering a bona fide (real) job which requires a Bachelor's or higher degree or the equivalent and that they be willing and able to pay prevailing wage for that job in the area of intended employment. In my experience, USCIS does seem to raise more questions for newer companies, and due to perceived higher instances of fraud may ask for significant documentation from certain software services companies.

Good luck!

There is no grace period. However, if it is done right, you should be able to transfer without any problem. Our office has successfully processed hundreds of H1B transfers although the word transfer is "misplaced" in similar cases.
Good Luck
Shah
peerallylaw.com