Assuming your friend is of level to get all those quests, and is willing to do the prerequisite quests in the zone, the only quest he would not do is "Onu", which is a Teldrassil quest.
If he wants to do everything, start with Buzzbox 1, checking the furbolg camp, capturing a bear, and checking out the beached sea creature. (Return to town.)
Second, swim out by the dock for Washed Ashore, kill threshers as you swim north for Buzzbox 2, and then run over to Bashal'Aran for the quests there and finish up with the crystal.
Third, go back to the crystal and turn south to Ameth'Aran. Kill furbolgs in the camp for How Big a Threat? and random rabid bears for Plagued Lands and go back.
Fourth, pass by Bashal'Aran to complete that, and continue to the den mother cave and the mushroom cave. Go up to the end of the river and jump off the bridge to the waterfall to bottle some water. The third buzzbox is here for your moonstalker fangs as well. Kill crabs to the west of the river on the beach, and follow the shore back to town, looking for beached sea creatures. (Cave Mushrooms opens up the quest to see Onu and get the Master's Glaive. I mention this because it isn't at all obvious.)
Fifth, go south down the road and visit Onu at the Oracle Glade. Kill moonstalker sires and grizzled bears nearby for two quests, and head into the Master's Glaive to place the scrying bowl and collect the book. (Do the escort quest if you've got some assistance.)
Sixth, go north up to The Tower of Althalaxx, and proceed to the Ruins of Mathystra after that for the relics quest. There is one beached sea creature on the north beach you probably haven't seen, and there is a gnome standing on a rock at the far north end that gives you the two Gyromast quests. Do the first one.
Seventh, go south down the coast and grab whatever sea creatures you can find. There are 5 in all if you're feeling daring with the level 20 murlocs. Come in-land when you've had enough and find Remtravel's Excavation Site for the Absent Minded Propsector. Whether or not you actually try until you pass the quest, move east when you are done to where the polar bear is on the road, marking a cave for you. Do Escape by Stealth unless you think you can handle fighting out easily enough.
That should just leave Gyromast's Revenge and Vast Ocean, Deep Sea. DO NOT DO VAST OCEAN! That quest is allegedly level 14 or 15, but I have wiped on it repeatedly at level 19 **with a group**
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