You should be able to get a California license as soon as you enroll in a DUI class and to to the DMV with proof of enrollment. A first time DUI class in California is not that bad, most programs cost less than $200 and you do not have to complete it before you get the license.
No you will have to take and eventually complete the DUI program that the DMV is requiring you to take. You should be eligible for a restricted license once you enroll in the DUI class. Most states now are aware of the restriction in another state. The best thing to do is get this behind you and sign up for the program.