Good questions! But I have answers only to some of them 
Actually the transition from DBC to DMC is pretty easy. Most of the components from the DBC exist in DMC but it has much more of them and some of them are really fancy. There is also a lot of stuff integrated in the components so there is no need to write your own callbacks to controll som behaviour (i.e. the Accordion component - you do not need callback to open it).
And talking about styling it is one of the strongest sides of the DMC library. I am a pythonista with no experience from web developement. Everything I know about web developement I know it from Dash. So the concept of css styling sheets and classes seems so unnatural to me because I love to have my styling in my python code. What I love to do is to change the stylying just of the some exact component and not all of them. And this is really hardly achievable just with style because it can only access the root properties. And here comes the styles prop. For example if you have dropdown component (or select in dmc world) with styles you can access also the styling of the list that appears after click and much more. There is a part of documentation about it:
I also wrote one topic about it with the example I worked with in my work.
Talking about themes there is MantineProvider component in DMC where you can override the default behaviour of styling of the components for the whole app. I am not sure if there are some style sheets for DMC, maybe @AnnMarieW could help with this because I believe that she is the author of some of them for DBC 
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Regarding DashProxy and DashBlueprint I can not help because I am not using Dash Extensions yet