Maybe this is the simple key to our happiness - the things we will miss the most. They are the things that made us most happy - the things that enhanced our inner joy.
You've got inspiring thoughts here. Happiness, being a mental state, is free as you've rightly noted. On whether it can be bought, I think you're also right in a way. One can actually buy some kind of happiness with money. However, there are over one million reasons to be happy or sad. In reality, no one can be absolutely happy or sad. I think happiness comes in different sizes from having dreams coming true to having healthy body and relationships, etc.
So money can buy some kind of happiness but not all. I once stumbled on a funny quotes that says Money cannot buy happiness but I will prefer to cry inside a Ferrari
I once saw a quote that said - Money cannot buy happiness but neither can poverty