These "quests" are made by Dr. F. The way you get the items is different for everybody (it depends on how you play and where you go).

1st Quest: Fix the Broken Compass for Richard
Baffling Battery
Mysterious Magnet

2nd Quest: Fix the Helicopter

3rd Quest: Create a mecha-dog to help you find the Villain
Bewildering Balancer
Sly Sensor
Dark Dynamo
Stupefying Speaker
Perplexing Paw