Alex,
I am glad to hear you are going to be working with the Pro SDK. We have had quite a few people successfully migrate their ArcMap add-ins to Pro. To answer your question about the equivalency of the Pro and Arcobjects raster API's, the current Raster API in the Pro SDK is a very small subset of the ArcObjects Raster API.
1.) The Core.Data.Raster API is not equivalent but a very small subset of the DataSourcesRaster API. Please let me know if you find something missing. A lot of the time what you need can be accomplished in a different way. If not we usually prioritize what goes into the Pro Raster SDK based off users requests.
2.) Yes you will have to use the RasterCalculator_sa GP tool in the Pro SDK to perform map algebra calculations.
3.) Yes you can execute tools from Data Management and Spatial Analyst in the Pro SDK. I would also suggest checking out the ImageAnalyst tools if you have the Image Analyst extension.
The main thing to be aware of when migrating is that both SDK's are completely different and the functionality offered by the Pro SDK is still catching up in some areas. Working with the Pro SDK is not to difficult as Mathew commented (Thanks Mathew) so you should get up and running pretty quickly.
I hope the above helped answer your questions. If you have any more please let us know.
-Prashant