What effect do the low noise adapters have? Noticeably quieter or just barely? Significant decline in cooling ability (CPU runs hotter)? I'm finally about to order this thing and trying to get a better understanding of whether or not I should use the adapters.

How does the push/pull orientation work? Does the 120mm fan push air down onto the heatsink while the 92mm fan pulls air up from the CPU to the heatsink?

I'm new to dual fan CPU coolers.

Both fans pushes the air down towards the CPU. This configuration is often called push-pull, since the first fan pushes the air into the heatsink, and the second fan pulls air out of the heatsink.

If you use the fans like you describe you'll end up with a tug of war situation; the fans work against each other.

Push is usually more efficient in quiet systems than pull, which is good to know when using a single fan.
It never hurts to try different setups tho, especially if you have a PSU with a fan right above the heatsink.

In short: always make sure the airflow direction is the same for all fans.