Oh my! Those are awesome!
So let me tell you - the tall ones are usually harder to bloom and they need more time to be mature. Some even 60 years (not yours though).
The smaller ones look very cute. The one with flat stems is an Opuntia.
The little rounder one could Echinopsis. They usually have stunning huge flowers that last only one day.
On the second photo you have Echeveria and Aloe.
Make sure they have very well drained soil and are watered only after the soil is dry. I killed some of mine with overwatering or when they were getting a bit too much rain. They hate to get roots wet for too long. Maybe that was the cause of the death. Such pity - they were gorgeous!
Thank you very much for sharing your experience with cacti. They are very helpful and informative. My wife now is even more determined to expand her cacti collection.
Meantime thanks for identifying the species. Will be Googling them in a while. Also thanks for your time and visit. Very very much appreciated.
I am more than happy to help out with what I know :D
Cacti are awesome. Even if they will not bloom for you I am sure your wife can grow them successfully :)
I know she'll give it her best as she always does. Thanks again @ewkaw.