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If you're trying to root a plant with a woody stem, this may not be the best way to go. Softer, more pliable stems will root in water much more easily. Plus, be sure to change the water every 2 or 3 days. Here's an article for you: https://www.gardeningknowhow.com/garden-how-to/propagation/cuttings/plants-that-root-in-water.htm

If the plant you're trying to propagate has a woodier stem, here's an article on how best to do that: https://www.gardeningknowhow.com/garden-how-to/projects/rooting-plant-cuttings.htm

The best method will depend on the type of seed in question. Many plants have different requirements (Like cold stratification or scarification) that must be met in order to grow.

Here is a collection of articles to get you started:

https://www.gardeningknowhow.com/garden-how-to/propagation/seeds

Since we don't know what you are hoping to graft, I'm giving you a link to a page that contains articles about grafting different kinds of trees and plants. I hope this will be helpful: https://www.gardeningknowhow.com/search?q=grafting

According to a plumeria society you shouldn't water after the initial watering till new leaves have grown, which indicates root development. You also shouldn't move the pot or remove the stem from the soil. Since you did remove the stem, was the tip soft or black at all? If so it is rotting from too much water. (Overwatering is the top reason cuttings fail.) You can cut off the rotting part up to white, hard wood and start again.

Was the stem seeping a white substance? I've read that it does contain a white sap that flows when the stems are cut. Not sure why the top should seep.

If your cutting still looks healthy, I would try again in new potting soil (two parts cactus mix to one part perlite). Moisten the soil before inserting the cutting and don't water again till 2 leaves develop that are one to two inches long.

There is a Plumeria Society in Encinitas, Calif., that may be able to offer more help if you haven't already contacted them. https://southerncaliforniaplumeriasociety.com/

Some plants are easier to root than others, but here's an article with general information about rooting plants from cuttings. You can also search our site for instruction on rooting specific plants.

https://www.gardeningknowhow.com/garden-how-to/projects/rooting-plant-cuttings.htm

It is hard to get every cutting to grow successfully. I'd suggest you nurture the ones that have sprouted leaves and dispose of the dead ones right away. Or, you could cut off the dead ends, re-dip them in the rooting compounds and keep trying. Just be sure they haven't contracted any pests or fungus before you rejoin them with the healthy ones.
https://www.gardeningknowhow.com/garden-how-to/projects/rooting-plant-cuttings.htm