That is opuntia (probably Opuntia microdasys?). All those new pads should be wider, similar to older pads. ..."ton of new arms"... is not really sign of well grown plant if they are skinny/narrow. I do not grow it, but believe that they will stay skinny, and really should be cut/broken off since they are too weak to support further growth. Pads that are removed will grow roots (that is how you propagate them), but IMO the skinny ones should be discarded. Plant is not receiving enough light - you need to keep it where it does. Otherwise, skinny growth will continue. Plant should look like this (photo from the net):

If succulents start collapsing/leaning, and there is no rot (there could be but maybe you don't see it yer) it is often because of poor root system that is not supporting and anchoring plant sufficiently. Roots could be dry or rotting, depending on if soil is too wet, or too dry. Show us the clear pic of it or at least describe. Also, pot plant is potted in needs drainage hole(s). What is the soil like? How much and how often do you water? What kind of light is it getting?

BTW, those glochids are hard to remove from the skin, so be cautious when handling. Wear very thick gloves (leather is good) or use rolled-up newspaper to hold the pads...

I find that leather is skin and the needles will embed in it and it is a good way to ruin gloves. News paper is better. also elders or wood glue dried under heat and then ripped off like a band aid will remove the glochids. Thin growth due to lack of light is call etoliation. I hope I spelled it right.

"Thin growth due to lack of light is call etoliation. I hope I spelled it right."

Close!! :-) Etiolation.

There you go.

WOW gardengal! I have been both spelling and saying it wrong for YEARS!

Thanks for the correction!