Can I connect the amp to my computer and record my guitar? how can i do that?
Yes, you can. Just connect the amp to PC with mini USB cable (NOT micro USB, commonly used fo smartphones, tablets etc.) and install a DAW application. I recommend Audacity - for free, very powerful and easy to use.
Yes. I just did this with my Code 50 and Garage Band. Connect the USB, then go to the settings of your computer and make sure the input selection and output selections are set to CODE, which should appear in your menu once it's connected (along with your other settings like "headphones" or "USB 1", etc).