According to the
Exxon - Mobil synthetic-lubricant recipe book, not only that synthetics have viscosity-index improvers (VIIs) but Group IV synthetics have more viscosity modifiers than the Group III/Group IV or Group II+/Group IV synthetic blends.
Therefore:
Myth 1: Group IV synthetics have no VII: false
Myth 2: Group IV synthetics are better than Group III synthetics: false
Myth 3: Synthetics have always less VIIs than dino: false
Myth 4: Group IV synthetics have always less volatility than Group III: false
If you go through the Mobil recipes linked above, you will see why these myths are false.
This is not to say that all synhetic oils have VIIs; there might be Redline or such that have none but chances are that Mobil 1 etc. that you are getting have plenty of VIIs; in fact possibly more VIIs than good dino oils.
Coming to the first question: No, 0W- is not necessarily better than 5W- or 5W- is not necessarily better than 10W-. Yes, the fuel economy and cold-start performance will be better but there will be compromise with the NOACK volatility, high-temperature performance, and oil durability. This is not to say that there is no 0W- oil out there that outperforms 5W- oil in all respects but just be cautioned and at least check to see if the oil meets all the manufacturer standards you need.
Bottom line: Oil blending is more of an art than science. Oil manufacturers will blend things any way they want and chances are that you aren't getting what you think you're getting. Synthetic, Group IV, etc. have little meaning and your best way to ensure that you're getting a good oil is to make sure that oil officially satisfies the standards you need, you looked at UOAs, and went through the user posts here about others' experiences (which you should take with a grain of salt). Then you can buy and try it and even do your UOA and be your own judge.