In your first four examples, #1-3 are felicitous (stylistically correct/normally formulated, at least according to my dialect of American English), while #4 is not.
- This is the same car that you bought me. Only one car exists: the car in front of us now is the exact same car you bought for me in the past.
- This is the same car as the one you bought me. Two different cars are being referenced here: the car in front of us now is the same kind of car (most likely the same make and model) as a different car that you bought for me in the past.
- This car is the same as mine. Same as #2. There are two cars, and the one in front of us now is identical in some way to a different car that you own.
- This is the same car as you bought me. Not felicitous as written. It could be rewritten as either "This is the same car you bought me" (no as, equivalent to #1) or "This is the same car as the one you bought me" (equivalent to #2).
In most cases, using "same as" makes it clear that you're comparing two different objects (although the word order also matters). Without the "as", the meaning is more ambiguous. I think the intended meaning is pretty clear in your example #1 above, but this is not always the case. For example:
This is the same car I had (when I was) in college.
Here, the meaning is ambiguous. It could be interpreted as being the exact same car (I had it then, and I still have it now) or merely the same kind of car as the one I used to have. However, I think most people would assume the latter, since there are other ways to phrase the former statement - e.g. "I've had the same car since I was in college" - that sound a bit more natural. I can certainly see situations where you might use this phrasing to talk about a singular entity, but I think it's more commonly used for comparisons.
This (car) is the same as the car I had (when I was) in college.
Unambiguous. This car is alike in some way to a car that I had when I was in college, but it is not the same car.
In the context of cars, I think most people would assume that "sameness" means the same make and model. You could qualify the statement by saying something like: "This (car) is the same as the one you bought me, only a different color." This tells the listener that you are making a comparison between (1) the car that's in front of you now, and (2) a different car, which the listener bought for the speaker at some point in the past, and that the two cars are the same in terms of some relevant details (presumably the make and model), except for the detail that was explicitly mentioned (the color).
As for your other examples, (a), (c), and (d) are felicitous and equivalent in meaning to #1 above (there is only one car). Examples (b), (e), and (f) are not grammatically correct. The last three all sound fine to me, and I would interpret them in the same way: there are two cars (his and yours), and the cars are identical in some way.