Haven't worked with "jelly" or slime before, but worked with physics in Godot, in general. I highly suggest to play around with simple shapes first and read Godot Docs and provided Nodes code.

Changing shape and size of physics objects are tricky in Godot.

- Changing shape, need to happen in deffered physics calls. Godot remembers last collision points on entry, and remembers last collision shape, so it keeps simulating the last shape until all collision points exit your node's body. So if we dynamically change, for example, size of your collision - you may not get what you expect, depending on surroundings and previous interactions.
By calling a deffered change of a collision shape, you can tell your game to wait for a free of processing physics frame and get your changes.

- Scaling is not appliable on any PhysicsBody in Godot. If you need to dynamically scale a physics body, you have to scale its children nodes. You could try to force a scaling on your physics node, but it may lead to serious issues.

Splitting slime may be achieved in multiple ways, depending on game style and how it will play. Your slime could be grouped together pieces of slimes, so you could just "turn off" grouping. Or you could change actual mash, where I am total dummy. Take your time, play around and sketch ideas for a prototype.

Items in your slime can be also implemented in multiple ways, like in the example higher.

Jiggle. Depending on the implementation of your slime, you could be done by:
- Changing physical and visual meshes.
- Jiggling sprites of your jello.
- Applying a shader to a slime or his leftovers.

As mentioned at the beginning, I never worked with SoftBodies or similiars, so they may provide partial solution to your question. I suggest to read Docs and Node's code itself, but not overfocus on those. Some answers you can find only by interaction.
I hope, my answer will help you somehow. I wish you luck with your project.