First, please accept my apologies for the delay. I was already offline when you responded hours later.
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ANSWER: I do not think you need representation. DUI's are not considered "crimes involving moral turpitude" unless there is an aggravating factor like getting the DUI while driving on a suspended license, or if someone was seriously injured or killed as a result of your DUI. Based on the fact that these happened so long ago, that you have not mentioned any aggravating factors, and that you have not mentioned any other crimes involving moral turpitude, you should be fine. Note that alcoholism is a basis for which I have heard of naturalization being denied. It will be important to your citizenship process to show that you now have your drinking under control.
As far as radiation treatments, no, that will not affect your eligibility to renew your Green Card or citizenship.
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