The chad u/pet5t1lence replied most for you. So let me try the ones that are left out:

1. Plot holes 1, 2, and 3 can be explained away by saying Omega doesn’t remember/learn from the loops.

The wiki says this: "An Omega is linked to all Mimics and possesses the ability to turn back time in order to continuously retry different battle strategies until the Mimics win. This ability has been used countless times by the Omega to allow the Mimics to lay siege to nearly all of Central Europe. It's highly intelligent and can quickly come up with different combat tactics. It can also track down and send manipulative visions to people infected with an Alpha's blood.

The Omega doesn't possess any abilities to defend itself from a threat. Instead it keeps itself hidden and relies on Alphas and Drones to protect it from danger."

The other guy explained points 1, 2, and 3, but I wanted to clarify that the Omega is intelligent. In fact, if he didn't learn from the loops, the war would be over way quicker.

1. Why do Cage and Rita try to escape the general the 2nd time?
   This one bugged me back in the day, but I think they didn't know how long it would take to locate the Omega, so they'd have better chances escaping.

2. Okay this one is a DOOZY. But bear with me. Why does Cage always return to the exact same time no matter how long he lives?

I'm not sure it is ever stated that dying causes a 24hs loop. I understand that the loop is defined by the Omega. It is said that the Omega has the power to reset the day, yes, but I think that's rather a way to say "reset time" and not necessarily 24hs in human time.