This isn't as hard as it seems when you're about to begin. Getting familiar with the current code base might seem very hard, but you just need to take short steps. You don't get to know a whole system in a week, but it'll all eventually come into place.
Try getting assigned easy/short tasks, specially if they require you to learn how the whole system is built. They'll probably do this anyways but, if you feel overwhelmed, feel free to ask your manager about it.
If your team is as teamworking as mine, they won't mind you asking short questions like "where is the window controller located?". These kind of questions will get you up to speed in a hurry! Also, get your hands in as much documentation about the project as possible. You should spend some time as soon as you arrive getting familiar with your team's workflow too. Just watch, ask and learn. It won't harm if you get to know a colleague who can guide you through this.
One important thing is getting information organized. I use Ubuntu's notes. I set up a new note for each subject and add as many little snippets of information as I can to it. Even if you think you'll never forget it, you will! Once it's done (or, for some reason, it's no longer something you must remember) just erase it. As as I finish some piece of work (or if it stalls for some reason) I take a quick tour over my notes, clean them and decide what I'm going to work on or research about.
I've been involved in projects with short iterations and a lot of time pressure and it worked for me: nobody expects you to get up to speed as soon as you arrive. Just relax and learn.
I think that learning new technologies (languages, libraries, version control systems...) is part of your career. I've always devoted my own free time to learn those, but you'll learn in work too! It won't harm using your free time too: you'll learn faster and, after all, it's a skill set you'll carry out from job to job.
As you said, you were very up front about your skills, so I don't think their expectations are that high. You might want to take advantage there: go above their expectations and they'll have a nice surprise.