As a VERY new beekeeper (I only got them at the end of July) I am a bit confused about feeding them. I've been feeding them 1:1 sugar solution since I had them. They look very happy and are well behaved. Should I continue with 1:1 or go to 2:1, and for how long?
The simple answer is - it depends!
1:1 syrup is something that the bees can use immediately so it is best for most of the year. However, in order to lay down winter stores, honey or syrup has to have it's moisture content reduced by the bees befoer it's capped, so it makes sense to give them the least possible work to do by giving them thick syrup. So from, say the middle of August, thick, 2:1 syrup is best. If all the sugar doesn't quite dissolve when you mix it up, then you can always sposh a little more water in, until it does, as the bees will sort it out. (Don't be too hung up on the ratios).
A July nuc is a fairly late one to get for a new beekeeper. How many frames of brood are there and is all the foundation drawn? And what hive is it? We will be able to answer better if you let us know.
(And have you treated for varroa?)