This is Echinopsis cactus :) they have huge flowers... when they eventually bloom.
The top is a little stretched - it means it needs more light.
The babies you could probably plant separately in spring. At least the bigger ones. If they have some tiny roots growing, the better. I would wait though until they are about 1cm across. They look a bit small.
The yellow bottom I am not sure. If it is soft it would be better to cut it as soon as possible right under those roots that started to grow there. Roots normally don't grow like that so I think there could be something wrong either way with the root system, or that thin bottom and the plant doesn't get enough water, so started to grow the roots from the middle to get extra support.
If you decide to cut it, do not plant it until the wound heals and dries completely. Even for a week or two.
Did it even bloom for you?
No, these cacti have not bloomed yet, my sister gave them to me last summer ... I try to take care of them according to your advice, I hope that in the spring I will wait for them to bloom)
Thank you so much for your feedback and great advice!
Fingers crossed :D
Thanks!