Ref the fan... The old days of the fan just running when the engine does is long gon. The fan is not connected to the engine and will often carry on running, or even start apparently at random as it is thermostatically controlled and will come on if there is a build up of heat under the bonnet.
I fitted some replacement LED bulbs to the DRLs today, and in the process of doing so had the bonnet open and started the stopped the engine a lot.... I noticed that "things" would start making noises on the turn of the ignition which certainly sounded like the fan, but it was always the same, so personally I would not worry, as per my comment quoted above, plus with the computerisation of cars, there is so much pre-checking of systems and functions, then as long as it is predictable, should be ok.
Ref strange noises ... Could this be a warning noise with one of the non-classic sound settings enabled? As mentioned, I replaced the bulbs, and when I turned on the lights for the first time afterwards to check, it sounded like I was getting a short-circuit and something burning up!! Ignition off fast and checked bulb. Turned out the lights-on warning when the "jungle" sounds are enabled sound just like a burning up noise (to me anyway) - could your noise be down to something similar?