I would say that it is entirely possible to be completely truthful without being at all honest. Generally you do this by answering a question exactly as asked, or by giving as little information as possible when you know something relevant that would interest the other person.
For instance, if your father comes storming into the house and demands, "What happened to the mailbox?!", you could be truthful and say "I saw that on my way in, it looks like somebody clipped it with their car." (After all, you did see it on your way in, and it does look like that). Or, you could be honest and say "My friend who was giving me a ride home wasn't looking when he turned his car around in the driveway and ran into it, and I told him not to worry about it, I'd take care of it for him."
So, for a definition, "being truthful" = "making only statements that you know or believe to be true", while "being honest" = "Telling the whole truth (that is, all the relevant information that you know)."
The definition of the two words makes them synonymous in virtually all cases. However, they do have slightly different connotations that lead to preference in usage. I generally think of something as "fast" if it can achieve a high speed. I think of something as "quick" if it responds rapidly to input. This generally leads to preference of one word over the other in context; "fast" is used in context of speed, while "quick" is used in context of time. So, you would travel fast to get somewhere quickly.
In the same vein, "quick" is used to describe the quality of an action that is short and powerful, e.g. a "quick head-fake". "Fast" is generally used to describe actions that are more sustained, e.g. "a fast sprint down the field".
None of this is concrete; you hear of someone, say in a race, having "the fastest time" much more often than "the quickest time". Clearly, the context is time, not speed, but use of "fast" is preferred anyway.
Best Answer
Quicker is the comparative of quick, which is an adjective; more quickly is the comparative of quickly, which is an adverb.
Informally, quick is also used as adverb, with the meaning of "at a fast rate, quickly." These are the examples reported by the NOAD (third edition).