Mars mysteries start between 1 and 15 Sols after certain requirements are met. Every mystery will grant a random wonder technology if successfully completed. If all wonder technologies have been researched the mystery will grant a breakthrough instead.
Can be failed
The Power of Three
Investigate the Mystery Cube anomaly (unlocks Dark Spectrometry technology)
Construct Project Morpheus within 20 Sols (random Wonder or Breakthrough technology)
Yes (fail to construct Project Morpheus)
Hard Mysteries mechanics
The Last War mystery features a mechanic called War Tension which measures how close the war on Earth is from becoming a nuclear war. It increases at a rate of 1% per Sol and can be increased or lowered by mystery choices. There are three possible outcomes of the mystery depending on War Tension:
If War Tension is reduced to 0%, the war ends with a peace treaty. Resupply becomes available at reduced costs, there is a spike in applicants, and one random technology is gained.
If War Tension doesn't reach 0% or 100% in 100 Sols, the war will end with the Second Cold War. Resupply becomes available but costs are increased by 50% for 50 Sols.
If War Tension reaches 100%, a nuclear war will start. Export, Research Outsourcing and Resupply will become unavailable. 50 Sols later contact with the remaining humans is reestablished. Passenger Rockets become available again but nothing else and all applicants will have the Refugee quirk.
Wildfire features a mechanic called Infection Level which measures how close the infection on Earth is from eradicating all humans. It increases every time an Earthsick Infected colonist leaves Mars and is reduced every time a Rocket loaded with the Wildfire Cure is sent to Earth. It goes through 5 levels, with the following effects:
Contained - initial stage
Endemic - export prices increase
Epidemic - applicant pool depleted
Pandemic - resupply costs increase
Extinction - most of Earth's population is dead and Export, Research Outsourcing and Resupply will become unavailable. 50 Sols later contact with the surviving humans is reestablished and Export, Research Outsourcing and Resupply become available again.
Between 10 and 30 Sols after the Marsgate trial if you exposed EsoCorp you will be notified that EsoCorp rovers are approaching Mars and gain access to the inexpensive Defense Turret Breakthrough. A few days later the first wave will arrive and EsoCorp rovers will descend all over the map. They will advance towards the colony and bombard anything within range with missiles, while Defense Turrets will counter them. It should be noted that Defense Turrets have greater range than EsoCorp rovers. The maintenance bar will act as a health bar. Once the first wave will be destroyed the second wave will approach but you will be notified that destroyed EsoCorp rovers can be repaired and used or salvaged for resources. Once the second wave is destroyed the mystery ends and you will gain the random Wonder or Breakthrough technology.
Metatron Ion Storms
The Metatron mystery will eventually start creating ion storms, artificial disasters that disables all out-dome buildings within a certain radius. Metatron sends up to five ion storms at once and each one continues for several sols.