I was wondering if light can be reflected how can someone reflect X-ray of what material does it need to be made of and is its design completely different to that of our original mirrors? Does this mean during long-space voyages in which radiation is an problem why can scientists not develop large panels of X-ray mirrors and Gamma-Mirrors and simply reflect the radiation off rather than worry about that?
Unfortunately X-ray and gamma mirrors are impossible to build the way you think - mainly because there is much less interaction with the matter comparing to UV - it will go through all materials commonly used for making mirrors. Even for EUV light (wavelength of 13.5nm) building effective mirrors is a royal pain.
As wavelength of X-Rays is very small (down to 0.01nm) you cannot build dielectric mirrors, as this would require depositing dielectric layers which are less than 1 atom thick.
It is only possible to reflect X-Rays at a very shallow angle (see Kirkpatrick-Baez X-Ray lens design), so you cannot use this for shielding of radiation coming from all directions. Gammas are even worse - the only thing you can do is to bring alot of mass.
Yes it is possible but as BarsMonster points out it isn't like an optical mirror. X-ray reflectors are used in the construction of nuclear weapons and are critical to increasing the yield. How they work is the initial fusion reaction releases high energy radiation, this is then reflected back into the reaction mass increasing the energy levels of the reaction mass causing a sort of radiation implosion.
Since these type of reflectors are typically used in weapons research there is not much public data on them. However here is a rough illustration of what an x-ray reflector looks like in the second stage (reference).