The most Resin-efficient purchase order at the Realm Depot is to claim the Magic Enhancement Ores every week, then the Wits, and then the Mora (assuming that the Traveler has already claimed the Transient Resin if they wish to).
For Travelers who wish to maximize Stardust and minimize Realm Currency: target Magic Enhancement Ores -> EXP -> Mora at Paimon's Bargains in the Shop. Inverse this priority (Mora -> EXP -> Magic Enhancement Ores) if Travelers wish to maximize Realm Currency and minimize Stardust.
The most efficient units for tree chopping:
Xingqiu (only if you manually time their attack string, spam clicking won't work)
The game can only remember the 10 most recently-struck trees at a time. After the 11th tree is hit, the 1st tree's state is wiped from the memory and can be harvested again. However, if a previously harvested tree is struck again BEFORE this, it will be moved back into the sequence as the most recently updated item. Partial harvests also count the same as full harvest or re-harvest.
Attacks that shake untouched trees, including enemy attacks, can allow them to be harvested using a small number of Elemental Skills in a short window. We explored this to find several things.
Shaking a tree marks it as a target for a wider variety of skills. Some attacks, like Mona's E, can only shake already-marked trees, and do nothing.
All physical damage sources & an odd assortment of character skills (Jean's E, Kaeya's Q) can shake/mark
Marks last a very short time
Some skills and Overloads can harvest. Characters like Bennett and Xingqiu can harvest using E skills, while Razor can harvest with E only if he uses Overload.