Clematis pruning

I got these last year from my local GC, when I didn't really know what I was doing (some might say that not much has changed!).

I thought they'd both had it, but they seem to have just died down for Winter. Should I prune it, or at least take off the dead bits - I read that you shouldn't prune them in the first year? Can I remove the supports to encourage it to climb the trellis?

Also, is the Pritzelago OK there? I got it to fill the space at the front of the container and I've grown quite fond of it, but worried it might end up competing for nutrients with the clematises, or will that be down to me feeding everything?

Ta, SJD