Need help identifying two cactus plants and a palm?

Kay
by Kay
Were new to the southwest so am always asking what it is that I have in my desert garden/yard. Have asked local nurseries about the two cactus but haven't found a name as yet. The palm may be a Sego but it's much bigger then others in the area. All plantings are about 30 years old so they are mature and in good health.

The first cactus.we have been calling a brain cactus because of the twisted branching and compact shape. Cactus stands about four feet tall with a pronounced trunk and segmented branches with small pink flowers at the end of the branch. Bees love them! When the flower fades a new segment develops. We have about a dozen of these ranging in size from 2' to 4' tall, and at least 2' to 4' around.
The next cactus is a variety of paddle cactus but has very long ears no unlike the burros in the area. Each "leaf" is at least 24" long. The largest one in the yard is about 7' tall and 15' wide. They get a dark red fruit but haven't tried picking them as yet. Again the nurseries couldn't identify them. We have a dozen of these also.
The palm that I've been calling a Sego is about 30' tall and about that much around too. The trunk is about 2-1/2' in diameter. This one "bites" with long 2' spikes and a very rough trunk. We have three of these. Again the nurseries wouldn't commit to the Sego name as they a much bigger then usual. I'm not too worried about their care as they seem to have done very well on their own. They are watered lightly about four times a month. Haven't considered feeding any of them until I can identify them, and do some research.
Any help would be appreciated?
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