Regarding the Moon landings, I don't think they could have been faked and the secret kept for 50 years.
The Apollo program is recorded as having employed 400,000 people across 20,000 companies. So you've got three main conspiracy scenarios:
Only a few top people knew there wouldn't be a landing? Well the people who designed the rocket are, well, rocket scientists. If the government asks them to build a Moon rocket they'll build a Moon rocket. Then the USA has a working rocket so why on Earth would they hoax the landing?
A lot of people knew there wouldn't be a landing? If you think a Moon landing is impossible, then you'd have to think that anybody working in the program who realised that would be bribed or threatened into keeping quiet. That's gonna be an awful lot of people. You think none of them would have gone public with their stories? Or gone to the Soviets? And yet to my knowledge, nobody advocating the Moon hoax hypothesis has been confirmed to have worked on Apollo.
Those jobs and people never existed? Well for one there's the money issue, so then you probably need banks and the IRS in on the conspiracy. For two reporters and historians have spoken to many people who worked on Apollo; to uphold the conspiracy that means getting more people in on it.
Then you've got other issues. The Apollo spacecraft sent radio transmissions back to Earth and pretty much anybody could have listened in on them and worked out where the spacecraft was. A spare Saturn V rocket launched Skylab which was easily observed from the ground and later re-entered Earth's atmosphere and pieces landed in Australia. The Apollo landing sites have been photographed by later probes orbiting the Moon.
The whole idea of faking a Moon landing and keeping it secret just falls apart I feel. Nixon was President when the landings happened and he couldn't even keep a burglary a secret.