1. This is one of the most important aspects of physics. Physicists are always particular they like to compare apples with apples and not with fruit salad.
The units of x in your equation is meters, m.
The units of u is ms-1 and time is s. When you multiply the two you get m.
The units for 'a' is ms-2 and t2 is s2 and when you multiply them you get m again.
Obviously the three terms all have the SAME units and therefore we can compare them.
2. I always tell my students that matery of vectors and units (dimensions) is a third of the battle won with physics. You must make a serious attempt to understand how this is done so that you can even solve problems that you have no clue about just by figuring out the units and dimensions.
A simple way of representing the dimensions of something is to put it between square brackets.
[t] is read as "the dimensions of time is"
Coming to your problem
[F] = [ma]
= kgms-2 (or MLT-2)
where you've written the dimensions as MLT-2 if you represent the dimensions of mass, length and time as M, L and T.
By the same token,
[t] = s or T
The dimensions of the equation on the left hand side is
[F][t] = kgms-1 or MLT-1
and the right hand side is
[m][v] = kgms-1 or MLT-1
which proves that the equation is dimensionally correct, because the dimensions or units are the same on both sides!
= [m][a]
= [m][v/t]
= kg[ms-1/s]
[m] = kg or M
[v] = ms-1 or LT-1