Can Ozone (O$_3$) form in a vacuum and if so can it deflect solar radiation
If this would work, would $O_3$ free-floating in very loose clouds in space help deflect solar radiation at all?


No, for many reasons:


Your cloud will disperse. That's what gases do in vacuum.
And then the dispersed cloud will get swept away by radiation pressure and the solar wind.
So you'll have to be constantly replenishing your loose cloud.
There are 3 billion metric tons of ozone in the Earth's atmosphere.
Compare that huge quantity with the 380.95 kilograms of lunar rock brought back by the six Apollo missions that landed on the Moon, or the 0.401 kilograms retrieved by Russia's unmanned Luna missions.


The engineering feat you are proposing is more than six orders of magnitude larger than anything humankind has done with regard to space. The Apollo program peak cost was a bit less than 5% of the total US federal budget. A factor of ten (one order of magnitude) larger scope would be far beyond the capabilities of the US government. Even with the entire world pitching in, a two order of magnitude increase would be nearly impossible. A six order of magnitude increase is economically impossible.

The worst part: Even if successful, your cloud won't do much. Oxygen in all its forms (atomic oxygen, molecular oxygen, and ozone) is nicely transparent in the frequency range where sunlight is at its peak. Evidence: You can see the stars on a clear night.