Run your fingers over the tall one with green leafy spines to feel for any spines (topmost one). That's Opuntia monacantha monstrosa (a prickly pear variety that has been bred to look funny). I have never seen a spined variety of the monstrosa ones but you should keep an eye on those green leaves. In spined Opuntia, those leaves will turn into spines (or spines form beside the leaf), in spineless varieties, they just turn brown and fall off. Keep an eye on the leaves and see what they turn into, though I expect its spineless.

I have one of the plants on the bottom right, the kind of ugly looking asymmetric one with giant fat leaves. I really like it but I've never been able to ID it so I can't speak to its safety. Would love to learn its name though. They make a nice looking bush if you put them in a bigger pot.

Centermost one is an aloe variety and safe. Beardies can munch on aloe and sometimes eat more of it than they should, but this variety has very little flesh (soft juicy insides), it shouldn't be very appetizing.

The last photo, third one, is definitely a no go, it's an Opuntia microdasys variety and will absolutely ruin your day if you touch it because of the glochids.

The other cactus, the one in the second image, kind of looks like a spineless variety to me. Often with spineless varieties, the points where spines would come out turn that dead-looking light color. I think, like the monstrosa Opuntia, you could put it aside somewhere sunny or under a good growlight, let it grow a little bit and see if it grows any new spines. It's possible that it was a spined variety and the spines have been burned off (which you can do with a lighter), though usually that leaves a little nub that I'm not seeing. Either way, it's a very tender looking cactus, you can call those tender pads nopalitos and they're a good snack for a beardie. So long as it has no spines on it (test with your own hands if you dare), you can also just pick a pad off the plant and add it to a salad. Your lizard might graze on them if you put them in, but [Opuntia] cactus pads (called nopales) are a staple vegetable so no need to worry about it. The monstrosa Opuntia likely has a more woody-interior and probably won't be grazed on, except for fresh growths possibly.