How many reentry permits can a green card holder get?

There is no limit to applying for reentry permits.

I am not aware of a limit to obtain a new re-entry permit. Please keep in mind you need to be in the U.S. to apply for one and get biometrics handled. That said, your time spent out of the U.S. will affect when you can apply for U.S. citizenship.

Generally, a re-entry permit is valid for a period of two years. However, if you applied and obtained a re-entry permit for two successive times, which would have resulted in four years, the third successive application will only be approved for just one year. In essence, in a period of 5 years, you can get two entry permits back to back for a period of two years per application and the successive third application will only be approved for just a one-year entry permit. Advisably, consult an attorney on this issue before you put your plan in operation.

The re-entry permit is valid initially for two years and can usually be renewed once for two years. Thereafter, it is only one year at a time. Not sure how many times they will renew it. This depends on the reasons provided.

Unlimited, but one must keep ties to the U.S. and pay taxes here to show you have not abandoned the green card.

It is valid for two years. There is no limit on how many; however, you might run into lack of immigrant intent and abandonment of residency issues.