1) If there is no gravity (which I have read a flat earth theorist claim) how do you explain gravitational time dilation?
Time Dilation is a Special Relativity effect as a consequence of accelerating frames of references. We don't doubt that in different frames of references time dilation occurs. I don't deny the experiment where a clock on the ground becomes out of sync with a clock on a jet.
In a "gravity field" the observers closer or further than the source are being accelerated at different rates in relation to other users, and thus Time Dilation will occur. Time Dilation will occur in a jet, a rocket ship, a "gravity field," and even a FE scenerio where traditional gravity does not exist and the observer is being slightly accelerated toward the stars the higher he goes. Time dilation occurs when observers are in different accelerating frames of references.
What
causes the acceleration is the question here. Gravity's mechanism as a bending of space as proposed in General Relativity has never been demonstrated true. There are contradicting theories for gravity, such as Quantum Mechanic's "Graviton" theory. Neither General Relativity (bending space) or Quantum Mechanic's Graviton puller particles really have any evidence behind it. The mechanism for gravity is not set in stone and, indeed, up in the air.
Observing starlight bend around the sun is as much a proof for GR Bendy Space as it is for QM Pully Particles. Nothing in the observation tells us what causes light to bend around the sun.
Hence, the mechanism for gravity is utterly unknown and undemonstrated.
2) If space travel is an impossibility then what happens to a space-shuttle once it leaves our atmosphere?
Since earth orbit is an impossibility it doesn't leave our atmosphere.
3) While I'm on that if space travel is impossible where did the lunar and mars rovers travel to?
They traveled to a movie studio.
4) I read the earth could be an infinite plain spanning in all directions, if this is so why has it never been observed to be so, yet we have explored and documented every part of the earth?
We have not explored and documented every part of the earth.
5) I heard one FEist claim that ancient civilizations had nuclear weaponry, do all FEists believe this load of crap?
I've never heard that argument.