Muggles writes:

Is time the same in outer space, or is it different?

Time is simply a measure of duration. The units by which duration
is measured are arbitrary, whether it is measured by physical phenomona
such as a full revolution of the planet (day), a full revolution of the
planet around it's sun (year/sol). Subdividing that into smaller
intervals simply requires a reference (e.g. the second, defined as

The second is the duration of 9 192 631 770 periods of the radiation
corresponding to the transition between the two hyperfine levels of
the ground state of the cesium 133 atom.


We count time
based on particular increments related to the Earth's revolving around
the sun, so when the Sun and Earth are taken out of that equation how do
we know that time in outer space is measured the same?

The duration of an interval is a function of the observer. Consider
a hypothetical spacecraft travelling through space at a significant fraction
of the speed of light. An external observer might experience a duration
of fifty years for the round-trip voyage, while a passenger on the
spacecraft may only experience six years in duration for the same trip.

Everything is relative, or so the great man wrote.

Consider, now, two spacecraft heading in opposite directions at,
say, .99C; What would the speed of spacecraft B appear as to an
observer on spacecraft A?


If the speed of
light is a means to measure time, does it travel in a straight line in
outer space or travel by a curve,

Light can, of course, be bent. An optical lens (e.g. in a camera) will
bend light towards a film negative or a CMOS sensor.

On a larger scale, something called graviational lensing takes place
which can bend light around massive astronomical objects (stars, galaxies,
clusters, et alia).

https://en.wikipedia.org/wiki/Gravitational_lens

Light, of course, may also be slowed. Consider light through a
non-vacuum medium (e.g. water or even fiber optics).

Light-year describes not a duration, but rather a distance.

OR is the speed affected by the
gravitational pull from the different objects IN space and that
gravitational pull can either either speed up or slow down the speed of
light? How can we determine the age of objects in outer space if we
don't have a valid method of measuring time?

Determine speed (relative to observer) of remote objects (e.g. stars):

https://en.wikipedia.org/wiki/Doppler_effect#Astronomy

Determine distance to star:

http://earthguide.ucsd.edu/virtualmuseum/ita/06_3.shtml

Given the distance, one can determine the age w.r.t the singularity.