From the drivers perspective - what provides the best illumination in adverse weather, in what position do lights get most dirty and restrict light output.

I'm obviously naive - designers have rarely concerned themselves with the mundane question - "what works best?"

Why the headlights in many modern cars started to go downward from bonnet level? Quite a few cars like Nissan Juke, Hyundai Tucson, Skoda Kamiq etc?

Traditionally the parking lights were below headlights, where as now parking lights are above headlights in many cars!

Is it just a fashion statement or there is some logic behind it?

Traditionally many 1940s and 1950s cars had sidelights on top of the front wings above the headlights (eg Jaguars, Austins, Rileys, the FordV8 Pilot. )

The sidelight position changed as the 'three-box' shape became the norm, mid 1950s I think.

And frequently cars in the 40/50s had a small prism above the sidelight so the driver could tell if they were illuminated

Oldest car I've driven is a Morris travaler and I remember the headlights being useless at best more like candles in jam jars. Is this why they had a prism because the lights made no difference to forward vision?

There will be a limit within the regulations where the lights will go, as well as the practicalites of the laws of physics and the lights needing to be able to point down the road.

I think the one key difference in the last few years is the now near universal use of LED lights. There is no longer the need for someone to get into the back of the light unit to replace the bulb as they are sealed for 'life' (whatever that turns out to be, fortunately the LED headlights lights in my wifes car have made it to 6 years old without any problem so far...). The LEDs themselves are also much smaller than any previous form of headlight bulb, even though most cars seem to need three or for minimum for each headlight.

The other driver, I suspect is the trend for ever bigger front grilles. Moving the headights down below the front grille means the grille itself can be even bigger, wider and more hideous. When the OP mentioned the Hyundai Tucson I was surprised as it hadn't struck me as a car with oddly placed headlights. I then searched on Google and realised they have just released a new one, with a truly horrid huge front grille which is nearly as bad as the one on the BMW 7 series....

One disadvantage of headlights being set low is the dazzle from reflections of puddles of rain, especially in potholes (unthinkable in Britain, I know...) and this is obviously problematic regardless of oncoming traffic. The same is true of low-mounted DRLs, most of which stay lit with the headlights on for some unfathomable reason.
Ironically, the raising of headlight height, in this case to meet 1975 US federal lighting regulations, was one of many nails in the coffin of the MGB. Since cash-strapped (bankrupt and then nationalised) BL couldn't possibly re-engineer the whole front, even for its biggest market, the decision was taken to jack the suspension up an inch, ruining the handling in the process. Anti-roll bars were deleted to save costs, rubber bumpers were stuck on and finally, power output was reduced by emissions regulations and a catalytic converter, so bye-bye MG. BL's remaining sports car budget was then pumped into the TR7, which had more than enough headlight problems of its own!

Positioning of all lights is determined by the Construction and Use Regulations. If you are v-e-r-y bored reading them will take quite a while! Available online.