Before this question can be answered clearly, it is necessary to resolve the usage of ba erev in the Bible. That was done last week. It means sunset. Then we find in Exodus 16 that ben ha arbayim follows sunset. So, clearly, that is the period of time between sunset and dark.
They were to keep it until, and to kill it at, ben ha arbayim. Okay, twilight has been clearly described, but here there was an additional factor. It is the word "until." The Hebrew word is ad (phonetically, in English); and it means "up to a specific point in time; not through, nor beyond; the limit of time itself." That came from Gesenius' Hebrew-Chaldee Lexicon to the Old Testament.
At the very least, that means that the lambs were not to be kept beyond the fourteenth (if we want to take it in its broadest application)—because the dating there would allow us maybe to think that the fourteenth would continue all the way up until the sunset. That is, the usage of the lambs, the killing of the lambs. However, when we apply what we know about ba erev—that is, the sunset of the thirteenth day beginning the fourteenth day—the killing of the lambs began the events of Passover at the beginning of the day. It does not terminate the events of the fourteenth. And "until" (that is, ad) seems to imply, very strongly, meaning the beginning of the day. It was to be kept until the beginning. So, the answer for element 1 is that the lambs were killed at the beginning of the fourteenth.
This is the Hebrew word shachat, which means "to kill." It is the same word that is normally used, throughout the Bible, to indicate a sacrifice (as at the altar). So, the Passover is to be sacrificed, and it is to be eaten.
I think that anybody ought to be able to see (looking at these things in their context) that keeping and eating are equated. Keeping the Passover means eating the Passover. And it had to be done on the fourteenth! Our Bible is the clearest evidence of this. Really, nothing could be clearer. Even our Savior was concerned about eating it on the fourteenth, and He did it correctly.
Symbolically (figuratively), killing the Passover emphasizes—to the person who is doing it—responsibility for the death of the Savior and, therefore, a recognition of sin. That is, that we are responsible for the Passover Lamb's death; and therefore, then, the payment for those sins is the death of the Savior. And that is certainly important. However, eating it (eating the Passover) emphasizes the more important continuance!