Why do many public places have their lights on during the day?

fluorescent lights last longer if never turned off and maintenance on them is always high so you actually save money by leaving them on especially if access is difficult , new LED lights will likely change that , currently their output is not high enough at low wattages to make a change always worthwhile

Thats probably a glitch in the photo sensor thats supposed to control when lights go on and off. On street lamps? The little sensor on top sometimes it gets dirty and cant tell when its dus or dawn so it stay on all the time.

So it's not dark inside

Because some places have limited windows, and can get dark inside even during daylight.

The outside lights? There's a program for them to be turned off and on automatically that malfunctions often. Some are controlled by photocells.

cos its below the minium light levels still

Not always as some turn them off to save electricity but some just don’t...