You may get some names that get close, but you're still not going to get solid IDs (you're talking tens of thousands of cultivars in addition to species, and hundreds are in mass culture) - I'm not even totally confident on saying what genera they are without flowers to give us a clue.
That being said as long as you don't care about having an exact name, looks like you got some very nice plants! Before they go anywhere near a frog tank make sure to remove all those water stains off them, hard to know if they are just from hard water or fertilizers - plus the plants will love you for getting off the crud getting in the way of them collecting light and respirating!
As for the pups... do you NEED to cut them off? Not enough people keep clumps of broms in their tanks IMO - even a variegated form is less busy and more "natural" in a tank all together than multiple different looking broms, and frogs love a good clump to hang out in. If it's purely for size, that's a bummer.
For cutting them off I'd go as close to the base of the Mother plant as you're comfortable getting. It should all be hard woody stock. This give you plenty of stolon to use to mount without risking getting close to the crown of the plant and damaging it. I would just mount it straight to the panels, and the best way to get the plant to grow directly to the panel would be to have the base of the plant against the panel which would also give you plenty of stolon to to use to hold it steady as well (tie it at a couple of spots on the woody stem makes it nice and secure, don't get too close to the base so you don't damage it). You'll want to have the plant as upright as possible to hold some water, and as the plant adapts it will learn to flare out more where there is light. With high humidity of most terrariums I would NOT put any moss around the base - you may just end up rotting the plant out. Where the crown (base) of the plant is in contact with the TF panel it will send out roots on it's own, and eventually support it's own weight. Make sure it's center always has water and it will be fine.