score:7
Surprisingly, the TSA must get asked this enough that they have entries on their "What Can I Bring?" FAQ page about them!
So, to answer your questions:
You will need to remove your printer from your checked luggage into one of the security trays, yes. It's considered an oversized electronic device, and the TSA's entry on printers does mention the need for this. There's no need to remove the ink if you don't want to, as the TSA does claim that they allow you to bring them in your carry-on.
(If you have TSA PreCheck, however, you may not need to remove the printer from your bag, as one of the benefits of PreCheck is that you don't need to remove large electronics. YMMV.)
Maybe. It's explicitly allowed, but I can't imagine that people often carry-on printers with them, so you might raise a few eyebrows. Print out those pages and have them on your person, and get to the checkpoint a little earlier than usual. Generally, with the "weirder" items, they don't do more than swab for explosives, but it's up to officer discretion. If it's suspicious in the eyes of the officer, even after a further screening, the officer doesn't have to allow it still.
I'm sure though at most large airports, the TSA officers have seen far stranger things go through the checkpoint, so a printer might not be that odd. Now if you don't mind me, I'll be in the security line with my TSA-approved carry-on live lobster.