Re q1 and q2: in special relativity the key invarient is the line element $ds$ defined by:
$$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$
In this expression the timelike dimensions have a negative sign while the spacelike dimensions have a positive sign, so in the above expression there is only one timelike dimension, $dt$. This is how we define which dimensions are timelike. I'm not sure what you mean by saying "the parallel direction is time", but this is unlikely to be a helpful definition. The negative sign of the time dimension is responsible for all the "weird" effects in SR e.g. time dilation and length contraction, and it also implies a constant maximum speed (i.e. the speed of light).
Re q3: adding a second (macroscopic) timelike dimension is mathematically possible, though as far as I know no GUT uses this because it leads to physically unreasonable consequences, which takes us to ...
Re q4: a second macroscopic timelike dimension allows closed timelike curves and hence violations of causality, so any theory of this type wouldn't be a good description of the universe we observe. Various ways around this have been suggested. Itzhak Bars has suggested a theory with two time dimensions - I don't know the work well enough to know how he gets round causality problems. F Theory can be interpreted as having two time dimensions, but they are not macroscopic so there are no causality problems.