Do LDS Missionaries have to file taxes while on a mission and no income is earned?

My son turned 20 this year. He is on missionary work within the USA, and not on my insurance (he is on the church's insurance, if any) and he is covered by Indian Health Services for being a descendent of a Native American Tribe.

Do I file taxes for him on his behalf? Zero income

Can I claim him on my taxes? - I think the answer to this is no, but just wondering if I am doing something wrong.

Can I get him on Obamacare under his own policy or together with his mom, who is on Obamacare?

Everyone lives in the same household