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.
the prices for items ordered from Lazada are include all taxes and shipping costs, regardless from where they are shipped. However, I don't know how they handle the custom clearance. It's not about deliveries from Lazada. Maarten mentioned there is a 0% VAT agreement between China and Thailand which is not correct. Any import is subject to VAT, regardless of origin and its just a question on how companies like Lazada handle the import process.
you need to pay VAT on everything you import. What you might referring to is the Form E (ASEAN China FTA) which regulates the import duties on certain goods.