Heat rate is the measure of the conversion fuel into sellable energy-power you can put on the grid and get paid for. Plant auxiliary losses and turbne and generator losses count against heat rate - fuel you bought and burned but that you can't sell as electricity to a customer.
Reactive power causes higher heat losses in the generator core which are rejected to your heat sink (as well as in transformers and in transmission lines but that is beyond the scope of the OP.) It takes fuel to generate the heat that is rejected to the atmosphere because of the heat generated due to reactive power. That counts against heat rate. Power companies (mostly) want to sell MW. If you are selling only real power, your best heat rate is when MVA = MW or PF = unity. That is when generator heat losses are at a minimum. Even if you are paid for reactive power, the generator heat losses caused by generating it reduces your heat rate.
To answer your second question, based on the above heat rate is affected by PF but not in any way proportional to it.
rmw
PD: I predict that this post will get my EE buddies stirred up so have at me.