Hi Heather, welcome to YT!
1 - I have a 10-year-old black lab, male. He is the most gentle, sweet boy in the world. How do Yorkies interact with other dogs?
I have 2 labs (1 more coming soon), 1 boston terrier and 2 yorkies. My yorkies have 2 totally different personalities one is what I lovingly describe as a diva, the other is just a submissive luvbug. The luvbug (Coco) get's along with all of the dogs, but she doesn't really interact with them as far as playing goes, she does play with Bella though (the diva) I think because she is way closer in size. Bella likes to be dominant and is strongwilled. She plays with my Boston terrier and 1 of the labs while in the house and being supervised. My other lab is older and not tolerant of puppies or small breeds come to find out 
so she just hides from them. One thing you have to be very aware of with large breed and yorkies is that accidents can happy very easily and a 60lb+ dog is huge compared to a yorkie.
2 - I have two young boys (4 and 6). I am, of course, a bit nervous about getting a small dog due to the fact that I have children, and this puppy will always be around kids. Obviously as a puppy, I am not worried, but I do worry that as it gets older, it will be grumpy, nippy, and not very good with kids. What are your experiences?
My 2 yorkies are still very young so I can't offer any advice with attitude and age in this breed. I have 5 boys (18, 16,11,5,and 3) they have always been around dogs, cats and reptiles and taught to treat animals properly .. and ongoing lesson. My worries wouldn't be so much with the dog as it is older but with making sure the children are good with the dog. Any dog is going to be a grumpy turd to a kid if it isn't treated nicely by said kiddo. I really think that as long as the kids respect the animals they will grow to love each other unconditionally 
3 - Are they easy to train? And what sex is easier to train?
They are extremely intelligent dogs, however don't expect potty training to come even close to as easy as it did with your lab. Maybe you will get lucky but I've noticed a good 98% of the yorkie owners on this board have had potty training frustrations. They do get there, it just seems to take more time.. and their bladder isn't nearly as large so i'm sure that may be why. As a mother to all boys my advice on male or female is FEMALE! You can do her hair!!!! You can dress her up if you want!!! Pink, Frilly... prissy... love it