Once a telescope is bought, Hazou could investigate how they work.
A simple experiment Hazou could do is to measure the speed of light.
The iron nerve is perfect for experimentation, since the same move will drop items the same way each time.
Dropping objects of different mass at the same time will let him discover that objects fall at the same acceleration regardless of mass.
He could also try throwing objects.
However, air resistance will force objects to fall at different speed. Hazo could experiment with this by modifying the surface area of an object.
With an implosion seal and an airtight container, he could experiment with dropping objects in vacuum.
Use Usamatsu’s Glorious Life-Saving Purifier to study the properties of the modified air. Some topics we could study are pressure change after use, effects of long term breathing (can be used to further munchkin out of game), flammability and other properties. It could then be tweaked and reexamined. Hopefully this would eventually give us insight as to what we're tweaking.
Instruments required would be airtight glass jars, and a way to induce a flame.
If we could find some way to discover electrolysis We'd have a method to isolate Hydrogen and Oxygen which could be used to tweak the life-saving purifier and other things.
An instrument he could buy is a compass.