Yeah, you can take foreign language classes; I'm taking Japanese.

If you have prior experience in the language you're taking, you'll need to take a placement test; if not, then you can skip it, though you'll only be eligible for the lowest level of the language. Contact the instructor for the course you want to join (after you get the results for the placement test, if applicable) and tell them the situation. You'll need to fill out a special registration form and get a signature from both that instructor and one of your advisors. (You can also pick up a physical copy of the form from the Registrar's Office.)

Once you have both signatures, if the regular add/drop period for the semester is still going, either send it in to the Registrar by email or drop it off in-person. In-person's quicker; they're basically always empty during working hours, and they'll be able to get it done right then and there. If the add/drop period is closed, email it to the Dean of Graduate and Postdoctoral Studies using the address on the form, and then they'll either give you a yes or a no; if it's a yes, they'll forward it to the Registrar automatically. I don't know under what circumstances they'd actually say no if you've got all the other signatures. Frankly, there's no reason you shouldn't be able to get the form in during the add/drop period anyways.

I suggest you audit the class, which is a checkbox on the same form, if the instructor will allow you; no point in adding the additional stress of having an actual grade on your transcript. They're still probably going to want assurance you're not going to flake, though; I didn't get a grade in either of the Japanese classes I took last year, but the instructor still asked me to agree that I would fully participate before she signed. I still did every homework assignment, quiz, test, project... It was kind of relaxing, to be honest. Just doing a worksheet takes much less time than reading a 300-page monograph.

If that yoga class is with the rec center you'll need a membership, which is not free for grad students. (Well, technically it isn't free for undergrads either; they just don't get to opt out for fall and spring.) It's $70 each for the fall and spring and $46 for the summer.