Im curious... you said he was AKC registered, but not purebred? How can that be?
He sure is a SUPER cutie and he does look all Yorkie to me. I couldn't even guess what he could be mixed with. I love the name Monkey!
You can still take him lots of places, just get a leash and harness. He'll just be your walker instead of your carry on!

I have a little boy and a bigger boy. I still take them together as much as possible and I usually end up carrying the little one and the bigger one walks on a leash. It works though because my little one is timid and my big boy wants to inspect everything! That's probably my fault though, I always carried my little boy and walked my big boy!
Anyways, super cute, and you'll love a bigger boy, they are rough and tumble, rugged and FUN!!! Yet still small enough to curl up on mama for a nap!
Oh and the not walking to his water dish, he could be nervous about flooring changes... until he gets used to it. Some pups are more timid and nervous to try new things at first. He'll get used to it!