wow wow wow.
too long and too many to read.
I see something regarding dimensions and speed + slowing down of time etc.

well.
first, get a clear glimpse on the word 'dimension' in physics.
what is a dimension?
quite abstract now.
we are living in 4 dimensional world:
3 spacial and 1 time.
in string theory it is predicted that the world has 11 dimensions,
the others that we can't 'see' are being curled up to Planck length.
so, traveling into another dimension?
not quite, you would have to shrink yourself to the size of 10^(-35) in order to 'jump' into the other dimension.

talking about the dimension of time and its property.
time can be associated with the description of 'arrow of time',
which literally means the 'direction' of time.
each spacial dimension has 2 way actually, forward and backward, which means 2 opposite directions.
but for time, it is only one directional, and the same direction as entropy.
so it is reversible.

time, is relative, not absolute.
it differs from different inertial frames of reference.
this is well explained in special relativity.
under the topic of time dilation.
we can slow time, and thus applying this to time travel.
we can travel to future.

and we are already applying it to our daily life if you don't realize.
astronauts or satellites above our head?
they experience weaker gravitational force,
and they are traveling at high speed,
these would result in time dilation and thus the time for the satellite will run at different rate as compared to those on earth.

however those satellites, especially those need to send real time information, together with 'time',
such as GPS.
the clock on satellite has to be synchronized with those on earth,
which means the times have to be the same.
if time dilation wasn't counted into the error and make corrections,
the whole GPS system would have been screwed up.
small dilation results in large change over time.

your time is 11.00a.m. right now.
the GPS sends you the real time-information of the traffic, but the associated time is, 10.50a.m. or even smaller.
however the little difference would mean a large fault in whole system.

erm this,
http://www.astronomy.ohio-state.edu/~pogge.../Unit5/gps.html
I've read thru it, and this source is reliable, the information is true.

if you are referring to traveling into the past,
I would say impossible.
think of this situation,
you are traveling into the past, in order to kill your father.
and then you see him, you're gonna shoot him with a gun,
but you succeed? okay let say you miss him for the first time,
then you travel back to that moment to do it once again,
but will you be able to kill him?
if so, then how are you born in the future?
if you are not born, how do you even exist in the first place to travel back in time and kill you father?
and what is preventing you from killing your father when you traveled back in time?
where's your free will?
as a human with free will, you should be able to commit your act independent of these 'destiny' of the time travel paradox.

traveling to the future is of course possible, as claim by special theory of relativity.

another issue, the arrow of time.
law of physics treat the flow of time equally, forward or backward.
the only physical law that seems to provide an arrow of time would be entropy, or second law of thermodynamics, it USUALLY increases with time.
however there will be rare statistical fluctuation in which the total entropy of the universe decreases, because there's a non-zero probability for entropy to decrease. for further reference read from The Fabric of the Cosmos by Briane Green, page 167