You don't every really know if they are fertile or not unless you watch the two mate! Even then there is no guarantee the eggs are fertile as it could be issues with the roo or hens reproductive organs. But most likely if they breed you will get a fertile egg 99% of the time.
Yes, let them be....nature is nature and I don't know any other way you could help them to breed!
Hatch rate? You can and cant do this.
Cant- There's always going to be a variation in hatch rates in fertile eggs, there is no way to change this fact. In saying that.....there is!
As a newbie this website is full of information archives, topics that have previously address your questions. but the short of it is there is no use repeating the same information that already exists in the other topics. So please search these archives and topics for the information of your curiosity.
You increase hatch rates and such by reading and learning as well as paying attention to the details. A good incubator, paying attention to the settings and making sure they are accurate.......etc will increase hatch rates. But you have to get the knowledge and experience behind you, eg learn what you are doing. Thus read the topics and you will be very pleased with the efforts.