--Any good places you are missing? Yup, you are missing lots - many beautiful Islands in the south, some great historical towns like Ayathaya, trekking up north, Kanchanaburi, Chiang Mai....... I would say that if you have chosen the places to go simply based on the fact that you know the names, than you should do some research. Phuket and Pattaya are popular beach resorts for a certain crowd, but they are also avoided by just as many tourist. I personally hated Phuket and will never go back, nor will I ever choose to go to Pattaya. However, there are many on this forum that love both. So before you decide where to go, find out what these places are like and what other options there are.
---How many days are enough? - well, Phuket and Pattaya are both beach resort areas. So it depends on how long you want to spend on the beach and partying. Neither of these places really have much to "see". Bangkok has some great sights and shopping that could take up two days or so. Some hate Bangkok though and prefer not to waste time there, but I tend to get stuck there for several days at a time.
---Can't help you with cars.
---Can't help with getting to Cambodia, but I'm assuming if you are flying than Bangkok would have the most options.
---Trains are good in Thailand and are a popular way to get down south or up north. Trains in Cambodia a very very few (I think there is only one weekly train left) and basically not a practical option at all. If going overland you will most likely be taking the bus.
---Phnom Penh is a somewhat interesting city with a few good museums and sights related to the Khmer Rouge, but the real tourist draw in Cambodia is Angkor. I would say at least 80% of foreign tourists in Cambodia are there specifically to see Angkor rather than Phnom Penh. I would recommend adding it on to your itinerary. Actually, if you only have 10 days and aren't planning on flying I would say scrap PP and just go to Angkor if you even have time to see Cambodia at all.
--- No, Cambodia and Thailand can't be described as "cold" at any time of the year. It may be the coolest time of year, but that means its about 25-30 degrees rather than 30-35.