how can I reduce manganese, hardness, radon, and prescence of coliforms in well water?
There's a good reason it's "an insane buy" but since you seem to be committed regardless (these things are why you pay an inspector and put conditions in the contract allowing you to walk away if inspection turns up issues...) There's no guarantee that a new well with solve any (much less all) of the issues, unless it ends up in a different water supply (not overly likely with only 4 acres to poke holes in.)

A persistent coliform problem requires chlorination or UV treatment. Chlorination and contact time (a big tank) will also deal with the manganese. The aeration that's typically used for Radon mitigation might also deal with the manganese, but you'll still need to kill the coliform if it's persistent, which you have to assume it is unless proven otherwise. A water softener will deal with the hardness; you may want a reverse osmosis system for drinking water (softened water has higher sodium from the softening process)

Radon is the most expensive and dangerous to deal with problem. You are probably best served to make the seller buy a commercial system, and then you need to make sure the system is properly maintained. Rather than repeat myself, I'll just link to the previous question about DIY radon water treatment and my answer to that. How can I build my own water aeration system for radon mitigation?

If you are going to buy the house regardless, get at least $10,000 knocked off for mitigating the well water problems.