You will have to read your health insurance policy to be sure. In most cases, local health insurance is NOT valid in other countries. Talk to your TA and find about travel health insurance.

Sometimes, yes....sometimes, no. Sometimes, only limited. You would need to check with your individual insurance policy on-line or call their information line. There are thousands of different insurances, and you may find that getting a separate "travel insurance" (available on-line) would be wise. These private policies are quite affordable.