OK here is the information you seek.
It's easy to find a parking space at one of the BKK short term car parks, much easier than Don Mueang. My preference is to enter the short term car parks at BKK (I think there are two opposite the terminal) from the 1st floor then immediately head to the second or third floor where there are more spaces. The other option is to enter the car parks from the 5th floor but if you do this you have to drive all through the 5th floor past many double parked cars (it can be tight) just to get to the ramp where you can down to the lower floors. I've never had a problem finding a space on floors 2,3,4. I usually go for floor 3. Floors 1 & 5 have the convenience of a walkway to the terminal. For the other floors you need to use the steps or lift to floor 1 or 5. You can park as long as you want but it's around 250THB a day.
Long term parking... I think as others have said it's around 140THB a day. There's a shuttle bus to and from the main terminal. When I used this option I took a Grab taxi from the car park to arrivals. It's about a 6 or 7 minute journey. On the way back I took the shuttle bus from just past where the taxis pick up passengers. There's a bus stop there. I had to wait at least 20 minutes maybe longer for the bus. The bus is free but you need to make sure you get the correct bus. The information is on the Airport website. Each parking space has a cover which offers some shade. There's plenty of space between cars so it's unlikely someone will 'door you'. After almost two weeks my car had a thick layer of dust all over it but you clean your windows and you're away. You just turn up and take a ticket. There's a person in the little kiosk. When you leave you can pay by QR or cash.
Long term car park location: https://maps.app.goo.gl/DAp6L77QzREasKmM6