Echinopsis aka Domino cactus belongs to the family of night-blooming cacti, meaning that they are pollinated by moths. It never ceases to amazes me that such small cacti make such large spectacular flowers that bloom only for about two nights, closing during the day. If you are up early, you can catch them at it
I took this picture 3 years ago of the leftover flower and the cactus body has fattened out a lot, it's a very old cactus, that's why it's brown at the bottom. It's not rot you are looking at but corking. I find this species actually enjoys getting watered well in summer so I leave it outside in winter and summer. The body swells considerably with summer rains but then it's quite deflated by the end of winter when I keep it dry.
It also blooms almost continuously throughout summer if it gets enough water, you can see the next flower bud forming.
Cacti are extreme and austere plants but they enjoy putting on a show at flowering time. This plant has surprised me: it was an unwanted gift, mainly because I was previously expert at killing cacti but this tough character just lasts and blooms without any fuss. I'm slowly getting more cacti and being more successful at keeping them alive.