Good descriptions. Your beer will absorb some co2, especially once you retap. Try that after it's been tapped for a couple of hours.
Also, you may have a leak on your coupler seal.
Click on replacement parts, part #9 is the seal. It could also be 4 or 5.
We see it a lot on worn old couplers where the coupler slowly leaks co2. An easy way to tell is to wiggle the coupler back and forth while engaged. It shouldn't have much give.
Because pressure is holding in your test #2 above, the only place it can be is the coupler seals or the beer absorbing co2.