Your first dolphin: Play through the first part of the storyline.
Other dolphins: Pet and touch the dolphins. When you get back to the boat, Kat might say it likes you. When you are asked if you want to make a new partner, choose "Yes"
and put in your partner's name. Have fun! :D
There are not any dolphin fish that I know of.
There are 8 different parnters in endless ocean. Rissos dolphin, common dolphin, bottle nose dolphin, false killer whale, commersons dolphin, white sided dolphin, orca and beluga whale.
Get the Medal in blue Hall.
it is in one of the caves in the Abyss
no, but you can skip the Bottle Nosed Dolphin.
To move the tree branch in endless ocean, you need to use the river dolphin. These can be seen in the temple in cortica river.
It is at the lower corner of the map. Hope this helps!
the grat drop off
click A&B to make it look like your grabbing something
go to the tools menu +, then press the food botton. shake the wii remote and you will be petting your dolphin.
To raise your dolphin's level in endless ocean, you simply have to work with it, teach it tricks, and feed it from time to time. It takes a LOT of time.(trust me I feel your pain.) Also, swimming with it wherever you go helps.
Animal friends ? Well I made one where a Dolphin was trapped and I leaded it out.