I have the quest to summon Echeyakee and 2 of my friends want him as pets. Can I abandon the quest and get it agian after one of them tames him?

And if Echeyakee dies in the battle can I still get the quest agian?

Yes to both questions.  So long as you haven't hand the quest in and completed the quest, you can resummon and tame him. 

Next time, please post something like this in the Hunter/Pets forum.