I have a special tool to clean the vertical blinds. It looks like this one https://www.amazon.com.au/Triple-Venetian-Cleaner-Microfibre-Cleaning/dp/B07TSK2DGX/ref=asc_df_B07TSK2DGX/?tag=googleshopdsk-22&linkCode=df0&hvadid=463557389968&hvpos=&hvnetw=g&hvrand=9547239927354811788&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9069315&hvtargid=pla-1206283036293&psc=1

I would either use a feather duster, which is time consuming, or vacuum them with the appropriate nozzle when they are shut.

I used warm soapy water (morning fresh) on mine for the greasy dust from the kitchen area, the bathrooms, i used a terry cleaning cloth to dust them first then the soapy water on anything that needed more attention.I did the same for my ceiling fans as well

Wipe dust off first and then use vinegar in spray bottle and spray lightly then give a brush off.

Have not had Venetian type blinds for awhile now but I remember that I made sure to vacuum them each time I did the room just to keep the dust down and monthly I used to carefully wipe each panel with a damp cloth- if it was to wet it just dripped everywhere and made more of a mess, so I also threw an old towel on the floor as I did this. I also dried each panel as I went to minimise risk of mould etc starting from things being left damp.

I recommend using white vinegar.
That’s what I use on my blinds (both wooden and vinal type).

Regular dusting with a micro fibre cloth is what I use on mine and warm soapy water if they are marked.

I used dishwashing liquid in a small bucket of warm water and cleaned each blade with a wet cloth. I then used a microfiber cloth to dry each blade otherwise the dust just sticks to it again. I have PVC shutters but imagine it should be ok to use on white timber as that are coated in paint. I found doing this meant I could just dust them most of the time. and every few months they get a ‘proper’ clean.
I assume the black speckles could be fly poo?

i wiped plastic ones with a cloth or took them outside for a hose.

I have this problem as well, Be really careul not to break them I have snapped a few of mine trying to get the what seems to be the sticky dust off mine. I find using something like mr sheen the first time and then wiping again with it at least monthly works. But is very time consuming. I would love to hear other peoples idea as with ours they are not able to be removed for cleaning. As i wouldnt know how to put them back up.