To your third point, investments in an inflationary environment are necessary because otherwise people would _lose_ money by doing nothing with it. It's better to risk for some return, than lose it by doing nothing. That's what separates it from an deflationary environment in that people gain more money by doing nothing with it. They don't need to incur risk to gain more.

This leads to your first 2 points, where people might still want to invest to get a potential higher return than the base deflation rate, investments would drop compared to an inflationary environment. In the inflationary environment investments are necessary to prevent the loss of value, whereas it isn't in a deflationary one.