Legal Question in Real Estate Law in Massachusetts

I don't see any reason why not, BUT this is the type of situation that is ripe for a co-owner dispute, buyout, or forced sale via the petition for partition process. Your tenancy may certainly be at risk if you rent an apartment form co-owners such as you describe.

Technically, No. Unless you have an agreement authorizing you to lease and/or manage the property, the owner's consent should be obtained in advance. If you rent the property without permission you are at risk of being liable to the other owner for any damages and to the tenant if the other owner seeks to invalidate the lease and evict the tenant.

You should obtain at least an email granting you permission to lease the property and under what terms, length of lease, minimum amount of rent, etc.