In a switched outlet, the following is correct:
The yellow light that comes on for "open ground" indicates whether an appliance will have power in that outlet. As you might guess, it is connected between hot and neutral.
The other yellow light is connected between hot and ground. It'll light if ground is good, but it'll also light in a number of nasty failure situations - Check out this link.
The red light is hooked between neutral and ground. It should not light because there should be very low voltage (not zero) between neutral and ground.
For outlet 1, the "appliance power present" light is always on. That says the switch doesn't work. It doesn't turn off power when you turn it off. It does seem to interrupt ground -- what the heck??? Can the switch be switching the ground? That's a very, very weird situation and I suspect you have a problem that exceeds the ability of the outlet tester. It's possible someone didn't want that outlet to be switched, and rearranged wires until it wasn't. Put it back. Or at least put the grounds right.
For outlet 2, it sounds like normal behavior if the ground is not connected.
I think it's time to shut off the breaker and pull the receptacles and switches out and have a looksy. If that isn't comfortable to you, then hit a library's home electrical repair section and school up.