How do I transfer my contacts from my phone 5s to my new iPad Air. Some are transferring automatically but most are not. Also, can pictures be transferred from phone to iPad?
If your contacts are stored within iCloud then simply signing into your iCloud account on the iPad will bring them over. If some are not, I'd recommend entering them into iCloud via the webpage. Having them stored in the cloud and synced when I sign in with my Apple ID has been a life/time saver.
Re: Photos
iCloud Photo Library syncs all of your across all of your devices associated with that Apple ID