This is a bit confusing. Taking the points in the order you mention them:
You signed the V5; you got a partial refund (and returned the car at this point, presumably), then taxed the car (why?) and signed the V5. (I'm not sure I have got this right.)
Then you say this: "I am worried if the people that i bought the car from so bad stuff with the car." What does this mean? What are you worried about, exactly?
I can't see that any of this would affect your licence, however. On the face of it, it seems this is just a deal that went wrong, but has now been resolved.
If you could explain a bit more clearly we may be able to offer further advice.
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