Do I really need...
 

Do I need to get flea controls for a 12 week old Yorkie? What about tick and parasite controls? And what about the supplement Nutrical? The vet I called said I didn't need the latter since dog foods already have enough supplements in them?

You will need flea and tick control if the dogs is going to be outside on the ground anywhere that these little buggers are (different types of ticks are indigenous to certain areas but fleas are everywhere). Age of the dog doesn't make a difference (pretty much all veterinary approved topical treatments are safe after 8 weeks of age). I highly reccomend getting the product from your vet (not a store or online vender) so you are sure you're useing the most appropriate product for his size. I know that my specific back yard hasn't had any fleas for the past few years, but if I'm taking them for a walk in the woods or to visit my mother's house, they will pick up fleas and ticks if I don't have Frontline (that's just what I choose to use) on.

Nutrical, if your puppy is eating well you shouldn't need it (breeders on here can give you more details) but it's good to keep on hand. It's a high calorie, high glucose suppliment usually used for animals that are not eating well, usually due to illness, but it's commonly reccomended for toy breed puppies since they're so small their blood sugar level can drop rapidly if they aren't eating frequently enough. Hopefully someone with more experience will advise you on the nutrical, but you should ask your vet too about useing it for this purpose and if they have alot of experience with toy breed dogs.

Congrats on your new puppy :D

Nutrical is good to have on hand. You don't absolutely need it if you have karo syrup or the like instead.

Really depends how many fleas are in the area. A 12 week old pup shouldn't be hanging out outside anyway, so it's more optional for now. The more your pup goes out, the more likely you will need it. If your vet is recommending heartworm preventative, then yes, you do need it asap. I know many people don't treat in CA because it's not a huge problem. I would be though.

Fleas don't have a minimum age limit for who they'll live off of so, yes!

Nutrical is good to have on hand. It's basically a pick me or to stave off hypoglycemia.

Your dog should be one HW meds which usually also control other worms.

Ticks- you have to decide if your dog is likely to get ticks (outside often, live in area with lots of ticks, walks through woods, etc)