Can Spartans Take off Their Armor?

Yes, Spartans can get their suits off, even by themselves.

Do Spartans ever take their armor off?

They practically live in their armour and hardly ever remove it. Their armour isn't grafted on, they wear a skin-tight undersuit (Which they are naked underneath) and the rest of the armour is attached on to that. It's kind of a ball-ache for them to put on and take off, and they feel comfortable in it.

Can Master Chief take off his armor?

In the video games, the Master Chief is rarely seen without his armor. To aid players in identifying with the character, cutscenes tease the character's face, but never fully reveal it; for example, at the end of Halo: Combat Evolved, the Chief removes his helmet, but camera movement hides his head.