I need to know the how and when of pruning this climbing rose. I'm tempted to trim off the spent blooms, but not sure if that is the proper way to prune it. Also, after a spurt, it seems to be slowing down, is that normal?

You can always trim off the spent blooms. Other than that no trimming is necessary except to get it to grow in the direction you want. I would not worry about it slowing down its growth; it looks very healthy to me.