Hello and welcome....Yorkies can be somewhat difficult to train, they are stubborn little mites! But there are puppy classes available to the novice, so yes you can train them. They love to be around their people and want nothing more than to please you...they are so very loving. I started with one and now I am owned by three!
As for leaving them alone, I work full time as do many here...its best not to leave them when they are young as they are prone to become hypoglycemic...if not checked they can go downhill quickly. If they must be left, an ex-pen is wonderful to keep them out of trouble....large enough for a bed, food, water, toys and of course pee pads.....you have come to the right place, any question you have will be answered...there are many wonderful knowledgeable people here, someone is bound to have an answer for you.
Keep us posted on your search, and again Welcome!