Looks like a Chenopodium or goose-foot.

If it is or isn't an avocado, I don't know. But it doesn't seem to be a succulent, so maybe you should post this in the Name That Plant forum instead. :)

Hi - whatever you've got on the very top of the soil (1st pic), that small gravelly stuff... as long as it's not from e.g. the roadside (could be coated in motor oil, etc.) and as long as you can find lots of it, it would probably be a much better mix for the tree. Just as is... providing fast drainage, which is all important for trees in small pots stuck on a bench (or... railroad tie?). Trees are not tomatoes and 'rich' soil and bonsai don't usually mix. I could guess at the name of it, looks quite familiar, but being way NE of you, don't want to guess wrong and send you down the wrong path for care. Thin plastic pots however, are not such great ideas (tho' good size drain holes are) because they flex too easily and roots, etc. get disturbed... they're ok temporarily, but not otherwise. Now, the fact is, that the trunk will fatten fastest if you'd have left it in the ground for a couple of yrs, and of course you can always replant and just leave a marker in place so no one accidentally mows it down or something, but that's up to you. Seeing as you're in a hot and likely dry climate, and it was surviving under a leaky faucet, you'll want to watch that it doesn't get caught in drought conditions, more so of course in a pot than the ground.

Hi Rob, I live in a area where there is very few garden shops unfortunately. There is one I found this year that has beautiful Succulents but only a few small cactus. They did not have any Adeniums at all. I actually had never heard of them until I happened upon these poor ones at Walmart just running thru the garden area one day. So glad I took a chance on them. Only issue I am noticing is one plant has some leaves turning brown on the tips then yellowing. Any idea what is going on and a solution? I just noticed it so I moved that one away from the others. The ones that have had leaves turning yellow before falling off are doing much better but they did not turn brown. It is frustrating living so far away from a area that we can't find everything we need. Can not find any "equal numbered" fertilizer like 20-20-20 except for 1 all purpose 4-4-4 which you sprinkle around the soil anywhere here. What fertilizer do you recommend? I am hoping Amazon has what I need simply because I can get within a day or 2. I am new this year to any type gardening be it inground or container! Sorry for asking what some might think are crazy questions. Your Adeniums are beautiful by the way!