Is the Cambodia road border open and are we allowed to drive to Phnom Penh or Singapore?

Yes the land border is open to the vaccinated. Unvaccinated quarantine for 7 days (zero with PCR test on the way back into Thailand).

Yes cars are allowed across the borders again at least some of them. Best one is Chong Chom for entry into Cambodia. Return to Thailand can theoretically be any crossing, such as Chong Sa-ngam, Aranyaprathet or Pailin/Pong Nam Ron.

This is for driving foreign cars into Singapore. Do also note that the immigration will also inspect your car for modifications or dark windows which are illegal in Singapore.

Hope it addresses what u need

If the car is yours and not owned by the bank, you can drive BUT there is hell a lot of paperwork involved. First, in order to drive to Singapore, you need to bring the car to Malaysia first, pay insurance and road tax, get your car plate sticker with English letters, check that your window tint is not too dark and so on. Then, at Johor Bahru checkpoints to Singapore, you have to get an Autopass card. I've driven Malaysia registered vehicles in Singapore and Thailand. I've driven Singapore registered cars in Malaysia. I've driven Thailand registered vehicles in Malaysia but not in Singapore, so not sure what you need to bring to get the Autopass. For Cambodia, I think it's not permitted to bring Thai registered vehicles officially. Better take a road trip within Thailand only.

Cambodia land border is open. At least for border bounces.