First of all, I think it's great that you are doing so much research ahead of time - well ahead of time - to try to choose the right dog!
Your questions are good ones, and difficult to answer because each little Yorkie can be so different! But there are things that many have in common, and you can read all the answers here and decide for yourself.
I am a relatively new Yorkie owner, but I will share some of my answers.
Barking: Lexi is not a big barker. She will bark if someone comes to the door, or if she hears something out of the ordinary. They are great little watchdogs and want to protect their families! She will also bark at her reflection in the back french doors, or the fireplace glass. It can be difficult to convince her that no one is there! She also has a very high-pitched bark when she want something. The time I hear this most is if someone comes home or gets up in the morning and doesn't get her out of her pen fast enough. It's not a lot of barking then, but those barks can really get right into your eardrums!
Medical/Health problems - There can be problems with luxating patellas, collapsed tracheas, and liver shunt. Those are the ones I've read about most often here. Since Yorkies are small dogs, wearing a harness and not a collar is often recommended to prevent damage to the trachea. They also think they are much bigger than they really are! Lexi will climb to high places, and wouldn't think much of jumping off. And she is a snuggler, but when she is excited or wants to get down, she can be very wiggly. This is extremely dangerous, as they can wiggle right out of your arms and do some serious damage.
Separation anxiety: No problems here, although if I have to gate her in a smaller section than usual (we had major construction done on our house), I would get that high-pitched yelp.
Chewing: Ahhh... Lexi is a paper shredder. That includes cardboard. And she likes to get into garbage. She has shredded a sponge once or twice. And she will pick up any small thing on the floor. I don't know how and where she finds this stuff sometimes! But then there are many things she will not touch at all. She will take socks only from the laundry - clean or not.
Energy: Yorkies can have high energy, and then can be ready to snuggle in your arms or in their beds. I know that when my husband is home, Lexi will often sleep all afternoon, as I'm guessing she does when he is working days. On weekends, she is out with me more, and tends to get tired earlier at night.
The yard sounds great, but watch out! My fenced in yard is not safe for Lexi as there are spaces she could squeeze out of the fence, and too much trouble she could get into!
They are such loyal little members of the family, and love to give love! I would definitely heed the advice of others and, should you choose a Yorkie in the end, start teaching your children early, and choose one that is likely to be a little larger rather than smaller.
If Yorkies aren't the dog for you, I had a Shih tzu for many years. She was so calm, not aggressive in any way, didn't shed, and was a great dog for a family.
Good luck!
