My theory is that the Ark project had been something that had been on the drawing boards ever since Shepard first came up to them with knowledge of the Reapers existence. The Ark was was constructed along with the Crucible, as a Plan B option should the Crucible fail to wipe out the Reapers as they hoped, but it's existence was kept quiet because unlike the Crucible that generated hope, the Ark would be seen as an admission of defeat.
There is no way an ark project and the crucible can co-exist, the crucible alone is enough to bankrupt the galaxy and all the galaxies resources are being thrown at it along with "any one who can hold a hammer." In addition the reaper's are destroying key instructor which is already taxing the galaxies logistics.
Shepard not knowing makes sense in the context of what they were doing in ME3.
Rumor's of the crucibles existence were spreading during the first few days of the war due to its scale. An ark project would be on a similar scale (since it would be a project with no room for error) so rumor's of its existence would spread eventually.
In ME3, Shepard was already in a high-pressure environment, with the fate of the galaxy being won or lost depending on their actions. They honestly did not need more things added to their plate, let alone know that the Ark was in place if they failed which might cause them to doubt that they were on a hopeless cause. Hackett flat out tells us our fervent belief in the cause is what is winning people over and securing their alliance with the other races, which is one of the reasons he picked us to be the Alliance's ambassador and pointman in the first place.
That's absurd, Shepard knows defeat is a real possibility even with the crucible (since they don't know what it can do). Its safe to say Shepard would have no problem knowing that there is a plan for the continuation of the various species in the galaxy should the crucible fail.
Furthermore, putting Shepard out there with the knowledge of the Ark would be a disaster should they succumb to Indoctrination, a possibility given the amount of exposure to Reapers and their technology in the past. The Alliance (or whoever builds it) probably don't want the knowledge of it's existence to be known outside of the project.
Shepard knows the crucible exist but is never told its location, the same can be done with the ark knows its exist but is never told its location.
Whereas the Crucible's secrecy is something Shepard can be trusted with. Despite the Alliance taking steps to keep it's existence secret from the public, they would have to know that the Reapers are probably already aware of such a device's existence from the Prothean extinction (and we learn later, the previous Cycle's attempts to build it). Furthermore, despite knowing of the Project, the need for secrecy is why Hackett does not allow Shepard knowledge of where it's being constructed at any point in ME3, meaning they could not lead the Reapers to it even if they were compromised.
See above comment.
It would be very in-character for the Illusive Man keeping that information to himself as he did with many of his other plans, since he had no reason to want to flee the Reapers if he could control them. Even though he was indoctrinated, he doesn't seem to have leaked the information to the Reapers... and even if he had, their typical arrogance would have the Reapers chose to ignore it as a threat to their plans.
TIM was indoctrinated long before ME3 if he'd knew about the ark so would the reaper's.
Liara knowing, but not choosing to inform Shepard probably was to avoid burdening them with doubt. She more than anyone would be aware that taking steps to ensure their civilisation continued if they failed was a prudent course of action, lest they share the fate of the Protheans and countless others. We even see that she had taken steps herself, such as with the time capsules, to try and make sure that something of their people would survive.
That's completely out for character for Liara, as I said before Shepard knows defeat is a real possibility even with the crucible and so does Liara. If Liara can tell Shepard about her data caches (containing warnings and the crucible plans) should they fail she would have no problem telling Shepard about an ark ship.