When you put Moga to nap in your home base they completely recover their HP and Ability points. The amount of time that the Mogas spend napping is dependent on the their level.
If you go to your friends homes and click on their trees with the bonus assault fruits you will get more bonus attack points.
Quest Items
Below is a list of quest items along with their location and how to get them.
Compromising Photos
Defeat Woolves in Spiral Cave.
Gertrude's Chocolate
Found in the Summerwind Fields when you defeat Wasabees.
Purple Pincers
Defeat Crabaos at Sandy Dock.
Starlight Lights
Defeat Twisters at Sandswirl Beach.
Star Seeds
A good strategy is to weaken your target before throwing your Star Seed because the weaker they are the easier it is to capture them.
Whistle Tree
Keep an eye on your Whistle tree as you must always harvest it on time. Failing to do so will result in it withering.
Zodiac
A good strategy is to catch Mogas of various zodiacs as each zodiac has an affinity to certain zodiac and vise versa. Try to have at least 3 different types of zodiacs at your disposal.