Many kalanchoes reproduce by growing 'babies' from leaf margins - some very many, some less. There are approx. 125species, and some are very prolific. K. delagoensis and K. diagremontiana are both referred to as Mother of Thousands (or millions :). Most other sp will reproduce very easy from any cuttings. Plantlets will grow from leaves just laying around like in post above, but not as many as two mentioned. K. prolifera is not as bad - but in warm climate may be considered invasive (like Nik posted before).

Ah, your mama is the unfortunate owner of a true garden thug, altho it is beautiful. This is goosenecked loosestrife, which has an inborn desire to take over the world. I have it, planted it deliberately many years ago and have watched its proclivity for domination ever since. I tried getting rid of it some years ago by digging and sifting the roots as thoroughly as I could. To no avail, really. It is back in all its glory. Unfortunately, it can and will send its runners into the lawn. The possible good news for your mother is that it seems hers is located between the driveway and what looks to be a sidewalk of cement (?). In that case, the plant may be effectively stymied in its spread. Make sure to deadhead the blooms before they can spread viable seed and just enjoy this pretty & unusual flower form in the meantime!

This lovely plant has come up at least 3 times in the last month. Pls. search for similarly named Peps here & you'll see. I don't have one yet, but it seems it's only a matter of time ;>)

There’s always Austrocylindropuntia subulata monstrose, but I don’t think that has a bunch of fuzzies like yours. Fuzzies is totally a botanical term ;). My guess is an Opuntia cross between subulata x vestita. I see it in stores as Austrocylindropuntia ‘Rollercoaster’. What gives it that real snowy fuzzy look is the Austrocylindropuntia vestita. It can take a ton of light/sun all day if you can give it or the new growth will become lanky.