I have not read anywhere in the SBD books or on the SBD website that one needs to count sugar grams in PH1. Being aware of them is good but the focus is really on eating more whole foods and having good carbs & fats.
As I understand it, the purpose of the PH1 restrictions on fruits & starches is to help purge your body of all the junk and high carbs/sugars in the typical diet. If your eating style before the SBD was not heavy on processed foods, loads of carbs and sugary items then the transition to PH2 should be fairly easy. If you were used to eating a lot of these items then PH1 is the quick way to get your body accustomed to eating properly.
As to your salad dressing quandary, I would use dressings that are diet friendly meaning low in fats and carbs (sugars). I grew up with Good Seasons Italian and just love it. It's one of the few packaged products I use. I make it with red wine vinegar and put water about halfway to the -O- line thereby using less oil. The <1g of sugar is very little. I would not worry about the 2g of sugar in the balsamic vinegar either. Those minuscule amounts combined with the sugars found in dairy & veggies still add up to very low sugars. JMO...YMMV
Congrats on getting thru day 1!