There's no definate "heat" issue based on brown fluid. If you smell cooked fluid, then I'd say yes. Brown though..that's usually the color of the clutches. And clutches do wear...like brake pads. We don't say the dust on wheels is from heat and pads, it's just the pads. In this case.. just the clutches Ma'am. lol
On the 6 vs 3. 6 is the latest and greatest. It's not necessarily the best, it's the replacement that GM has out.
I use the Coastal (Autozone) fluid commonly as it's one of the thicker fluids out there. Works well for me in transmissions. I've only put 6 in a freshly built trans. And the results are similar. Heck..ScottyDoggs brought some fluid from Tractor Supply. IIRC the price was right.