I believe have the same 7.5 pot and burner (both stainless) that your are referring to, I use mostly when brewing outdoors. It is the older version of this one
(the striped down model $169.95). I have had it for 6 years, I have made countless turkeys many fish fry's and 15 of so brew sessions. I like the stainless burner housing no paint to burn off and on rusty steel.
As for the pot, I have brewed with mine on my gas stove top. But before I go any further I would not recommend boiling large volumes of liquid in a narrow footprint to height ratio pot in any house where small children are present.
Our gas stove top (Whirlpool I think) has a "power burner" which the spec. states that it puts out 12,500 BTU's. I experimented before brewing and found it took 1.5 hours to bring 6.5 gallons of 60 degree water to a rolling boil. I would recommend putting 4.5 gallons of water in your current pot to determine if your stove is capable of first getting that much volume up to boil.
Now you can test our your cooling method on the boiling water, I use a 50' X 1/2" immersion chiller, with 54 deg. tap water I can get it to 70 deg. in under 20 min. Hope this helps. Good Luck.