I want to play my old game from my iPad on my my new iphone. So I want..

to do this you need to login to Game Center before you start Hay Day on the new device for the first time. If you have already started a new game on the new device, try deleting the app, logging into Game Center with your old login, then redownloading it. You should be prompted to transfer over your game when starting.

So login with your iPad Game Center account, download Hay Day, then play - you should be asked to transfer the data.

Why I can't play the same level and the same farm again
,

This does not work.

Sign into facebook on both devices and gamecenter, youll be sure to have the same level,m just did it with my ipod. Even if youve started a new farm, it will give you a confirmation notew after youve signed into facebook onto your need device. Just hit "Yes, load game" and voila!

This is rather challenging for children less than 13 years old!
Where does the HAYDAY app store game progress on an iPad?
A backup of the old iPad should store the game progress so the user should be able to continue at the same level when the backup has been restored to the new iPad.