Identifying this succulent
 

Hi, could someone identify this succulent for me please? I've scoured the net but can't find anything, even though it's a pretty common plant.

Will those young plants sprouting off it fall off, or do I have to cut them? Also, what are the white dots - they wipe off whatever they are

Thanks

Is it a Jade plant? If it is what's wrong with it? lol

It's definitely a crassula of some sort as far as I can tell online, but I haven't seen any with shoots like that, assuming they aren't babies, or root structures coming from the nodes