Points 1 & 2 is the same with mine, except the '2 click rule' only applies if locked/armed for a certain period of time, ~5 minutes or more, & only if I want to open the door immediately.
eg, If I lock the doors & then unlock them within a few minutes, I only need 1 click & can open a door straight away without tripping the alarm.
If I lock the doors & leave for a decent time, I can use 1 click to unlock & it will disarm the alarm if I don't open the door for maybe 10 secs or so.
If I want to unlock & open the door immediately, I'll need 2 clicks.
Point 3 doesn't happen to me. It all sounds a bit quirky - not sure why it is like that, but I don't think about it now, just click twice to be sure.
If you want to change it, I suppose a replacement might be the only way.
Cheers, Leon.