I'm looking at replacing the gas heater with a newer Rinnai heater for the safety concern of using half a dozen space heaters.

I work as a technician at Safelite replacing/repairing auto glass and my wife works as a CNA. 

But a bit of advice if I may, nothing replaces the personal attention that’s needed to gain the confidence of someone to sign your offer letter.

Can I use that as a bargaining chip on my inspection contingency by telling the seller: "Look, I will be ok with x that needs to be replaced based on the inspection but because of the radon mitigation I want $x amount off the property" or would that be illegal/breach of contract because I technically waived that particular contingency?

If you are realistic with both, the 1031 rules give you plenty of time to locate the replacement property.

If it is broke, either fix it (see #1 above) or replace it (#2 above). 

I once replaced a smooth top electric stove with a coil top.

I am confused on whether I should move forward and replace carpet and do the mold test or can hold off as they are leaving as per the co-signor.

The "Own in Ogden" (in my experience) has helped widows shore up some structural sagging and maybe replace a roof here and there.  

I had to replace them for the rental I have.