Is the absorbent substance in nappies biodegradable?
To keep it simple: there are as many different polymers as suppliers of the superabsorbent polymer used in diapers.https://en.wikipedia.org/wiki/Superabsorbent_polymer#Current_synthesis.

So, answer to #1. Some are, some aren't. As far as #2, define what you mean by "biodegradable". Take a diaper, put it into a composting bin, and turn it over every week for a million years, and I'd expect little to remain. It is likely based on your question that you are unaware that some diapers are marketed to be "biodegradable" and some aren't. The reality is that the term has no standard meaning - it's marketing hype. However, it's also true that some polymers will be inherently much more prone to decomposition than others and that some of these are incorporated into some diapers. 

Your best bet is to call (or visit) the customer service of the specific diaper manufacturer you are interested about. Note that the nih link provided in a different answer doesn't mention any use of the sodium salt for any major brand.  Pampers (P&amp;G), I think, dominates the market and sells 9 different disposable diaper brands. I didn't see any mention on their site about biodegradability, which was an important controversy some generations back. Since even "highly biodegradable" materials can take centuries to decompose in landfills, the question is a bit meaningless. (If you want biodegradable, use toilet paper (not seriously, since TP is designed to fall apart rapidly, too rapidly for practical use in a wearable product).)