He should have several fresh (as soon as possible after they are passed) stool samples submitted to his veterinarian to be sent to the diagnostic laboratory for a parasite check. Puppies can have protozoa parasites as well as worms. You can also use a worming medication like Fenbendazole or Pyrantel to treat him for the most common worm parasites in the meantime. These are considered safe to use in puppies according to Plumb's Veterinary Drug Handbook.
Because he's had abnormal stools his intestinal bacteria population may not be a normal one, and you may need to replace normal gut bacteria with a probiotic, such as Proviable, Benebac, or Fortiflora.
Today you can start Kao-pectate (kaolin and pectin only products are safe even for puppies) at 1ml per pound or 1 tablespoon per 15 pounds of body weight every 6 to 8 hours. This is quite safe and will coat his irritated gi tract as well as absorbing bacterial toxins. You can use it for several days until his stools look normal. You can find kao-pectate at the drug store.
You can also try feeding him a bland diet of 2/3 boiled, white rice and 1/3 boiled lean hamburger or chicken in small meals several times a day. Since you are seeing blood in his stools adding 1 tablespoon of pumpkin to his meals as fiber soothes an irritated colon. Ideally he should be eating a puppy food now, and that is what you need to transition him to as his diarrhea clears, but for now it is more dangerous for him to become dehydrated because he has diarrhea so we need to get his diarrhea stopped.
If he stops eating, or starts vomiting he needs to see her veterinarian as soon as possible.
Advantage is effective but it can be irritating and drying to his skin/coat, so that may be why he is so itchy. And it doesn't help to just repeatedly treat him.
Please realize that only 5% of the fleas live on your animals.
95% of them (eggs, larvae, hatching adults) are actually living on the environment. So if you have an active flea problem and don't treat the environment it will take a long time to resolve.
I recommend that you vacuum your home like crazy, throw away the vacuum bag in a sealed garbage bag and treat your environment with an effective area treatment like Siphotrol Plus II Premise Spray. It should be used every 2 weeks and no vacuuming for 2 to 3 days after using it to allow it to settle in. It has both an adulticide and an insect growth regulator so larvae and eggs don't mature. See this link for more information: http://www.drugs.com/vet/vet-kem-siphotrol-plus-ii-premise-spray.html
A premise spray is better than bombs because a premise spray can be directed into areas that flea bombs miss, like under cushions and furniture as well as along the baseboards where fleas and their eggs hide.
Of course you need to treat outdoors with a product that kills adults and inhibits development of eggs and larvae as well. Areas with direct sunlight will have faster degradation of products, and heavy rains will wash the product away so you may need to treat more frequently.
Best of luck with your pup, please let me know if you have any further questions.