I would love to know how companies can grant equity (vesting over time) to remote contractors (i.e., without establishing a legal entity in the remote country.)
It depends based on the country. Some countries require an addendum to your stock plan, or other changes. So you would really need to talk to a compensation and benefits attorney to be safe.
Signing an option contract with a vesting clause. Nothing about options or vesting is inherently tied to employment.
Hazards abound if you're a US startup and have employees in other countries that might treat ISOs significantly differently than the IRS.
I don’t think you can grant ISOs to non-employees. That doesn’t stop you from granting simple options. (It will probably be a tax headache, however. Derivatives usually are.)