When capturing (DV), should I still see the video playing in the record monitor? It looks like nothing is happening, although afterwards I find that it actually has recorded to a file and I just need to add the clip back into the project. Is there a way to make it add the clip automatically?

Yes, you should still see the video in the record monitor while capturing.
In order to add the files automatically, there is a checkbox that should be enabled by default. But, the thing that is most overlooked, is that you must "disconnect" in order for kdenlive to collect the captured files.