1) Is it hard to “stabilize”?
Yes
- Does it degrade or precipitate? Under what conditions?
It degrades. Water and temperature presence are enough.
- Does it always change the pH of a product? Are there ingredients to add to prevent pH shifts? 
Yes. You need to add a buffer system

2) Is there any difference at all between the various forms of Urea: Hydroxyethl, Imidazolidinyl, Diazolidinyl, and Urea USP? 
Not every compound with “urea” in the name is urea! Check the molecule to understand. 
- Is one form more stable/easier to work with than others?
Urea is only one. 

- Do ALL forms of Urea release formaldehyde?
Probably