About the only way for your second and third scenarios to make any sense is if Bob is pretty sure he had received the email but is unsure as to exactly when he received it. Allow me to expand the scenario a bit to illustrate what I'm suggesting.
Suppose Alice has known about the email for some time, since she, Bob, and Charlotte are all in this scenario together in some way. When Alice and Bob bump into each other, Alice is reminded of the said email and asks Bob if he'd received it yet. Since the email, to Bob, seems not that important, or at least as important as it may be to Alice, he has to jog his memory as to whether or not he'd received the email.
Consequently, Bob says, in effect,
"I'm not 100 percent sure I received it, but since I'm pretty sure I did not receive a follow-up email, at least recently, I must have received the original email by mid-January, since the event Charlotte was emailing everyone about takes place on February 1. In fact, I saw Charlotte last week, and she said "See you at the event on February 1," and I said 'OK.'"
As for the word eventually, again it might be appropriate given the above scenario. The word would function as a simple add-on indicating the uncertainty of Bob's having received the email. Perhaps Charlotte is customarily late in sending emails, and Bob's memory isn't that good, so he figures Charlotte did send the email eventually, though he's not sure when.
As for the third example which includes eventually, it sounds very awkward, stilted. To correct it, you might end up with something like the following:
Alice: Did Charlotte send you that email last month?
Bob: No, but I'm sure she sent it eventually-by-January-15h, which was the cut-off date for responding to it, and I do remember having responded to it. I just don't remember exactly when.
In conclusion, if the above scenarios do not fit the circumstances, then neither your second nor your third examples would be correct. Moreover, they would sound just plain weird!