DHPPC as the dog vaccine, vaccinates against Distemper, Hepatitis, Parainfluenza, Parvo, and Corona.
It should not. Just keep a close eye on your dog for a day or so. He or she should be just fine.
Each specific airline has their own set of requirements. But forsure you will need to make sure all his/her vaccines are up to date ( i.e. Rabies, DHPPC, BORD). They will need a health certificate that u can uptain at your vets stating they are healty for travel. Some require recent deworming and proof of flea preventitves.. Check with your airline carrier for more details.