I didn't see this, not enough coffee I guess.
What kind of snails did you find?

I've layered confederate jasmine by just removing leaves and burying that part of the vine in the soil below or pinning that part in a pot below and keeping it moist
jolana

I'm not sure what sort of snail he is. He has a white shell, and the snail himself is rather...greyish green. The shell is about three-quarters of an inch across.

In my book all snails are bad. Feed him to the birds.
Even aquatic snails that eat algae (which is good) multiply way fast (which is bad) because then they eat the plants and they all make too much poop.

The lime can be rooted from cuttings. My experience with rooting citrus is that what works best is short cuttings (3-4 inches long)with the growing tip present. The cuttings should be green but a little firm. No brown wood should be present.

Is it a Mexican Lime (same as a Key Lime)? Mexican Limes are the small real juicy ones with thin peels. The larger, pulpier, thicker peeled limes are Persian Limes. If it's a Mexican Lime, it's easy to grow them from seed. They mostly grow true from seed. Most of the seeds in the fruit are nucellar. "Nucellar" basically means that they just went ahead and made embryos without bothering with all of that pollinating and sex stuff. Each seed contains one embryo. What happened is that an individual cell in the ovary decided to just turn into an embryo. So, they are genetically identical to the parent plant.

I've grown Mexican Limes from seed and they have produced plenty of fruit without being budded to a rootstock. Budding onto a rootstock is really not necessary if you are growing the tree in a container.