2010 Jeep Wrangler - did these repairs cause new problems?

question 1) within a month of bringing jeep to dealership for airbag recall service, the shift changer cable broke - any possible connection?
question 2) after having shift changer cable replaced [not at dealership] a week and half ago, the heat system does not work, i.e. blows barely warm air, but no longer hot - there must be a connection (?!)

  1. No possible connection, in my opinion
  2. Very unlikely to be connected, but until the HVAC problem is properly diagnosed, nobody will know for sure.

Does this vehicle have a floor shift, or a column-mounted shift lever?

I don’t see the logic trying to tie any of these events together… so just don’t try. These sound like entirely separate events not to be correlated in any way.

There is no connection.
On your 2nd question, try a back flush. It’s easy and quick to do. It’s 10 year old car.