1. I have a wood floors and it seems a little slippery for my puppies, especially when they get excited. Is this safe? I see them slip here and there while playing with each other and I'm afraid that they will break a bone or something. I also can't carpet the whole apartment so I'm not sure what my options are. I do have a carpet that covers 1/4 of the apartment.
A few throw rugs would help. I've had to do that, too. Mine takes off running and has run into things, therefore, the throw rugs.
2. They love playing with each other and at times they jump onto each other so hard that the other puppy hits his head on the wall/fence/wherever he may be. He gets up and continues playing but I'm scared he may get a concussion? I'm not sure if puppies are more immune to these type of falls bc they are animals.
You just need to supervise their play. Sometimes one is a little rougher than the other.
3. I also have a 5-year-old yorkie that's currently at my mom's house. When I was raising him I made available solid gold wee bit kibbles 24/7 and there was no problem in raising him into an healthy adult. However, I do see a lot of suggestions on here saying that the owner should feed them twice a day, etc, and no suggestion of leaving it out throughout the day. Is there a specific (unhealthy) reason why? I just refill both water and food and it has worked out fine in the past.
One reason many people like scheduled feedings is so they know when they will need to go potty. The other is like Brit said - some will get too fat and some won't eat enough. When you have two, it could be a concern that one may be eating and the other might not be eating and you might not notice? That is just a thought.
4. I just went to a vet for first time check up and the bill came out to $450 for both two healthy puppies in NYC. 
The checkup included first set of vaccinations and stool sample testing. I don't recall what I received with my first yorkie bc it's been so long, but I just wanted to know if that is normal. Also, the vet recommended getting the rabies shot after 12 weeks, is this true?
I forget now when they are supposed to have it. I would probably wait until 16 weeks.
5. Lastly, I'm planning on getting them microchipped. The vet says it is $70 and I'm wondering if it's reasonable. Also, is there annual fees I should be aware of? How old do my puppies have to be in order to get them?
I don't know of annual fees. Perhaps someone else may chime in on this. NYC is going to be much higher than smaller towns and rural areas.