First - relax.
Finally - if you decide this is something you want to invest in, read, read, read and ask questions. Learn the fundamentals of programming and get through some basic tasks, like anything it'll come with practice. If you decide it's not something you want to do - start looking for a new job, and be particular about the type of job you apply for.
There is a very good tutorial to start learning jQuery. You should feel comfortable enough after reading it.
This guide contains no "click me" examples. The intention of providing only "copy me" code is to invite you to try it for yourself. Copy an example, see what it does, and modify it...
1. How have you marketed your self (e.g in your CV)? Have you explicitly said your are a web developer OR a web designer?
3. If you got the job as a web designer then this is outside of your remit, and you should inform your boss as such.
It really depends on what exactly your job role is.
Being outside your comfort zone can be a good thing. My advice would be to start small and focus on the basics of what you're being asked to do. Try to define the skeleton of your project and do use the experience you do have to keep this in your comfort zone.
Keep a very frequently updated TODO list, and keep only small, achievable things there. This works like a mini-scrum, and often works great for a single developer.
Finally, know when you're researching versus when you're developing. When you don't know how to do something (say, with jquery), write lots of throwaway sample programs. When you've reached some comfort level, do it in the real code.
Overall, don't focus on the mountain, focus on the trail.
For what it's worth, my initial reaction to any assignment with a high percentage of unfamiliar technology is something like yours. As Tim says, first relax. No one is ever really productive on day 1 of a new project (well, at least I'm not...), and panic is really non-productive. Then start learning the code base you've been handed. JasonFruit and Max have given you some great advice. I've had to learn new technologies under the gun, and if I can do it, I'm confident that any reasonably intelligent programmer can.
So unless you lied in your interview (which I doubt from what you have written), it might be a good idea to tell your boss about your fears. Since you are just a few days there, it should be kind of expected that you need some time.
Consider http://www.manning.com/jQueryinAction/. jQuery is a really popular JS library and very powerful. This book covers the library in a very modular way and covers the prerequisite JS needed to effectively use and understand the jQuery in client-side RAD.
The second edition covers up to 1.4, make sure you read up .on() and .prop() and the deferred object.
Sleep when you get the chance.
Also you're always gonna meet new challenges in a new job, just don't get stressed out
And get some sleep --- you learn better that way.
First steps first. Get comfortable with source control, or make constant backups of your stuff - that way you can undo your changes - you can feel comfortable breaking stuff.
The best place to learn JQuery seems to be the JQuery site itself — it's surprisingly easy to pick up, just give it a few days and don't worry about it.
I'm a firm believer in keeping the management (i.e. "your boss") informed about your work issues, and this would certainly count. A good chat with him/her would at least alleviate some of your stress! Finally, the other great advice about embracing this unknown is well worth heeding. Provided your boss interviewed you properly, perhaps he/she sees potential in your skill set!