could be biggibum, hard to tell from those wilted blooms.
to answer a few questions,
you can cut the spike (flower stalk) and leave an inch or so, it will not flower from that one again.
so far your plant looks healthy, but i suggest to let it dry out sometimes, having it sitting in that water tray is not good, they also need some dry period, meaning once a week a good watering should be enough, in winter time less.
i dont think it needs to be repotted, however, you can cut the new growth from the base and make sure there are roots attached to it, sometimes you can gently twist it.
maybe others have advices too,