I have been playing Warhammer 40k for over a decade but am not a complete authority.
Yes, a Space Marine can remove his armour according to the Deathwatch core rulebook.
The Deathwatch core rulebook's armour section explains that it takes around 30 minutes to remove or put on power armour with 3 chapter serfs (slaves). In an emergency it can be done in 10 minutes with one serf, but no less than that, as the proper rites must be observed.
I ran a Deathwatch game on a ship where they were not in their armour and had to either put it on or fight without it - very fun and lots of RP opportunities.
In the third Grey Knights novel, the main character is captured by Chaos and made to fight on an arena world. His armour is taken and the book deals with him adapting to not having it.
Do note that when he gets it back near the end of the book, he carries it around, refusing to wear it until it can be purified by the tech-adepts. When he is forced to wear the storm bolter gauntlet it burns his skin.
Space Marines are trained to maintain a state of readiness so would remain in their armour at all times unless there was a point to removing it such as repair.
Space Marines have many enhancements such as extra organs and equipment built into their armour to deal with anything not related to killing the emperor's enemies, such as cleaning, eating or sleeping. They can do their activities in armour, they just don't have to.
As an aside: Space Marines don't have sex - they're eunuchs. Being genetically engineered to kill, genitals aren't necessary.
Yes armour can be removed, check deathwatch core rulebook.
Armour is taken with weapons when captured but is very difficult to get back on in this situation.