Surprise Gardening When All Other Efforts Fail

I really want to grow plants here in the city. I don't get a ton of light so it's a bit difficult. I don't have roof access or a balcony. I'm not opposed to using the fire escape, but other people are... I also have cats so I can't have anything on the window sills. That leaves hanging pots and I have several in each window!

But nothing seems to grow. I've tried growing herbs from seeds. They tend to sprout and get about 2-3 inches tall. I feel like a proud mama and then... they die.

Thinking the problem was that I can't grow from seeds, I bought healthy looking plants. They lived a bit longer, but ultimately they died as well.

I can't say that nothing is growing in my apartment however. I have two accidental plants (and one bonsai tree that's taking over my hallway).

First up is my little lemon tree. I can't remember if this pot originally held a pepper plant or a bean plant, but regardless, it just had plant remains. One night I was chopping lemons and, on a whim, I decided to throw all of my lemon seeds into the pot.

I continued to water the pot, in case my original plant came back to life. It didn't. But! A week or two or three later, I checked and saw a bunch of tiny seedlings popping up from the lemon seeds!

(In case you're thinking of recreating this, I've heard that lemon seeds need damp soil to grow.)

I've been told lemon trees are bad luck and I should get rid of them, but I'm very proud of my little plants. I have no idea if they'll even produce fruit - but it made it through the winter in front of a cracked window so hopefully it will thrive this summer when it heats up.

Another surprise plant in my apartment was recently identified thanks to a friend. Again, I tend to water my empty pots in case a little seed suddenly decides to stop being dormant. And so this one did. As it was nowhere near anything I've planted, I was pretty stumped for a good while and because it turned such bright colors, I was momentarily afraid it was poisonous.

I think it's in the amaranth family and most likely a celosia. If it is a celosia, they can be used medicinally for worms, blood diseases, mouth sores, and eye problems. So. I've got that covered. The leaves are supposed to be very nutritious so I might try eating some since it just continues to grow.

Do you have any mystery plants? Any indoor gardening tips for the gardening-challenged?