Spoiler Alert! We have hidden this information so that you have the choice to try it on your own, or have the advantage of knowing how the sausage is made...
From the top of Earth's Tutelage it looks like you can get down and back up to get the snails. You will take some damage going down and there is no path back up the way you came. On the bright side, once you have walked out of the back canyon you will know the path and can just train through the lizards next time.
You can complete the Daily and Public during the same trip: Collect Mula Weed ×10, then kill 10 Rock Snails so you make Mushroom Weed Ointment ×10. Now you should be able to hand in 2 quests. Mula Weed ×50 and Rock Snail Secretion ×50 would let you do all 10 of your Daily quests (Remember, the max stack of both items is 5, so you will need 20 slots to get enough, or combine them as you go so you just need 12 bag slots open).
Daily Quests are repeatable up to a total (for all Daily Quests) of 10 times per day. The count can be reset to zero by purchasing and using a Daily Quest Ticket from the Item Shop (for 39 ($1.16)† ) or from any Phirius Merchant (for 780 ).
In all other zones they do not reward XP, TP or Gold, only Public Event Points. In all other aspects they are the same as a Daily Quest (except for the infinitely repeatable part and the rewards). Public Event Points contribute towards the completion of Regional Quest objectives, which in turn rewards a number of Energy of Justice commensurate with your amount of participation in the Regional event.
Mushroom Weed Ointment ×5
Rock Snail Secretion ×5 from Rock Snails northwest of Earth's Tutelage and 
Mula Weed ×5 in Xabu Village.
Daily Quest Ticket from the Item Shop (for 39
($1.16)† ) or from any Phirius Merchant (for 780
).
Dual-Function Daily Quest Potion.
Old Bag (hence the common sobriquet, Bag Quests). In Redhill Mountains, each repetition of [67][Public] Freedom Fighters rewards an 
Ancient Memento.
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