halacha - Does Neveilah/Tereifah make you Fleishig?

Another question asks whether meat of a non-kosher species (Behemah Temeiah or Hayah Temeiah) makes one Fleishig (considered to have eaten meat, so cannot eat milk). My question then is about kosher species that are slaughtered incorrectly (Neveilah) and about kosher species slaughtered correctly but found to be a Tereifah. Does that make a person Fleishig?

I don't really think it should matter whether someone ate the meat BeHeter or BeIsur. What seems to be important is the type of animal it is.

So:

1. 
   

   Meat of a Behemah Tehorah, slaughtered correctly, may not be eaten cooked with milk from a Behemah Tehorah.

   
   


2. 
   

   Meat of a Behemah Tehorah, slaughtered correctly, may not be eaten cooked with milk from a Hayah Tehorah by rabbinic injunction.

   
   


3. 
   

   Meat of a Hayah Tehorah, slaughtered correctly, may not be eaten cooked with milk of either a Hayah Tehorah or a Behemah Tehorah, by Rabbinic injunction.

   
   
   

   But what about:

   
   


4. 
   

   Meat of a Behemah Tehorah, slaughtered incorrectly or

   
   


5. 
   

   Meat of a Hayah Tehorah, slaughtered incorrectly or

   
   


6. 
   

   Meat of a Behemah Tehorah found to be a Tereifah?

   
   
   

In other words, such meat is totally not Kosher, but if you eat it anyway, are you Fleishig?

Furthermore:

If the answer to the above is no, such non-Kosher meat has no Din of meat and milk prohibition, then if you have a Heter to eat such non-Kosher meat, can you eat it cooked with milk?