I bought my wife a Fabia from 2015 and it does not have an AC (which she needs). 
would it be possible to buy a complete AC/heating system from a breaker of the exact same car model and install in on my car?

Yes but a divorce and change to a less needy, more appreciative partner would be less messy.

Maybe a really stupid question - and I'm sorry if it is, but in 2015, was it possible to buy a Fabia in UK that didn't have AC, maybe that car only has manual AC and not the fancy Climatic or whatever name Skoda gives its auto AC?

4 hours ago, rum4mo said:

was it possible to buy a Fabia in UK that didn't have AC

Yes. on the S level it was an option.

 

Thanks. AG Falco

 

Oh well, that clears that up for me.

 

So for this owner, a very silly mistake at initial purchase.