I think it is a good idea to cut back the flower spikes to allow the plant to grow. The flowers next time will be larger and the plant stronger. I recommend cutting the spike off about an inch above where it exits the plant. Others cut below the third node down to see if they get a branch and more blooms. This is fine if you have a really healthy, strong, phal, but most young orchids need to be cut back to allow them to develop roots and leaves.
Yes, now is a good time to repot. You should always fertilize your orchids. I recommend doing it weakly-weekly.