When most orchids have finished blooming, the spike should be cut off with a sharp, sterile blade as close to the base of the spike as practical. Phalaenopsis will generally rebloom given a little extra care. It's a good idea to cut the spike off entirely by mid summer to allow the plant to grow strongly to produce next year's bloom. Yes, if anything, flowering plants need extra fertilizer. Fertilizers meant for other types of plants are too strong for orchids and my burn the roots.
Orchids generally are light feeders but like to be fed consistantly.
Be sure to read the dilution directions on the container and follow them. In the case of orchids, more is not better. Once every seven to ten days depending on season and dryness of the home. In spring and summer, the plants need more water because they use more and the home is dry because of the air conditioning, in winter the plants use less water and dry out slower. Never allow any orchid to sit in water.