If your Arizona license is suspended or revoked due to the two DUI convictions, than it is unlikely that you can obtain a California license. The Department of Motor Vehicles in California should require you to turn in your out of state license, from Arizona in this case, which should be valid at the time.
All states are linked to the National Driver Register (NDR), a database of problem drivers. A problem driver is one whose license has been suspended, revoked, canceled, denied or has a serious traffic related offense conviction. If you do not inform California of your licensing issues in AZ they should find out by check out the NDR.
Now if your DUI issues in Arizona have been resolved and your driving privileges have been reinstated there, then you should be able to contact the CA DMV to apply for a driver's license. You should also be able to obtain insurance if you have full driving privileges, though your AZ DUIs are likely to affect your rates.
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