How does upgrading socketables work?

I’ve read the Torchlight 2 wiki page about transmuting and looked around elsewhere. I understand that in order to upgrade socketables, one needs to bring three socketables to a transmuter.

In my experience, transmuting three level-8 "specks" of different types results in a different (randomly-generated??) level-8 speck, but transmuting three level-8 "specks" of the same type results in a level-22 chip of the same type.

How does this process work, exactly? What rules are there?

Along those lines:

1. Is there any benefit to combining three unlike socketables besides getting a different socketable?
2. Can non-gem socketables be upgraded?
3. Is there a way to influence the odds of getting a particular type of socketable?
4. Is it true that the quality/tier of a gem can only be improved by transmuting three of the same type of gem?