Yes you get friendship points if you are playing the team instance with a friend.You need to be doing group convoys, team instances and so on with a partner. I'm pretty sure watering their tree and sending them flowers, by clicking on their name on your friendlist and picking gift flowers, you can only send 1 a day each worth 10k and that also registers to the popularity ranking.

You c*so kill monsters in the world with friends to earn friendship points as well. It's a bit tedious, but doesn't cost anything and can be used to level up characters besides your main.

thanks guys,i will use this info :)

Does FP help rank up???

whats the purpose of sending flowers to a friend??

it increases the friendship pt between you and the one you sent to by 1.
This is mostly used in VERY early game, when you have no lv 5 friend yet. This helps you and a partner get to lv 5 friend ASAP for the 5 extra Team instance runs.

There are other perks to having high lv friends but most of those aren't particularly useful/important.
There is also titles for the person who receive the most flower, but that's more of an ego thing.