Interior lighting issues

I have a few questions about some interior lighting (possible) issues on my car.

First, unfortunately I cannot remember when the light around the ignition key switch is illuminated or should be anyway. Mine illuminates when I press the key-less entry unlock and goes out when I start the engine and remains out even if the parking or headlights come on. It turns back on when I shut the engine off.

Secondly, I cannot remember if the little red light(s) in the transmission selector in the console that show which gear you are in is supposed to be lit up all the time (i.E. Anytime the engine is running) or if it only should be lit when the parking or headlights are turned on. Currently, it only lights up when the parking and headlights are turned on.

Lastly, I am having and intermittent problem with all the interior lights. Sometimes when I press the key-less unlock button to enter the vehicle or turn the engine off to exit the vehicle the interior lights do not come on at all but other times they do. All other functions on the vehicle seem to work fine.

Any thoughts would be appreciated!