As Suki said both are correct here . To American the distinction would probably be whether there was a specific due date for the project . If it was due close to the day you are making the statement , we would use the simple past, if there was a long period of time during which the project could be posted we would use the perfect tense. Actually if the proff is showing the projects of other students already , it suggests due date is past or very near. Ex : Where is your project? It is due today. --I didn't post it yet, now I will get a bad grade because it's late. Where is your project? -- I didnt post it yet--well hurry up, you only have until the end of the day. Where's your project ? I havn't posted it yet, we have until the end of the month to submit it.

'Post' is a slightly odd verb to use here. Are the students expected to post their projects on a school website, for example? Or sent it somewhere in the post/mail? It's not clear, but we'll stick with your example, for the sake of simplicity: You could say either 'I didn't post it yet' ( only correct in US English) or 'I haven't posted it yet' ( correct in both US and GB English). The form 'haven't post' doesn't exist. As for the questions, both are correct, but it would be more normal to use the present perfect. If you say 'Have you posted your project?' implies that there's a 'yet' in your mind, for an unfinished period of time. This suggests that there is still time for the other student to post his project. 'Did you post your project?' suggests - to the GB English-trained mind, at least - that you are dealing with an finished period of time, and both the speaker and the listener know this. Maybe the deadline for submitting projects is finished, and the speaker wants to know whether the other student managed to post his project in time or not.