No, it is not true.
ratio that compares 2 quantities measured in diiferent units
For measures such as parts per million, both quantities MUST be measured in units with the same dimensions. Here one is measured in micrograms (dimensions = [M]) and the other in millilitres (dimensions = [L3]).
In mathematics, two quantities are said to be in units agreement if they have the same units of measure. For example, if two quantities are both measured in meters, then they are in units agreement. If one quantity is measured in meters and the other is measured in centimeters, then they are not in units agreement.
If you intend 'dimensions' to mean units then whenever the two quantities are to be operated on each other then they must have the 'dimensions', refer to dimensional analysis
There are many instances: for example, speed is measured in kilometres per hour where the ratio is measured between a distance (measured in kilometres) and time (measured in hours). So it is no big deal except that you need to mention the units.
what is it
Its an inequality
A rate is a fraction that compares two quantities measured in different units. If the denominator of the fraction is 1 unit, the rate is called a unit rate.
no, cubic units are for three dimensional figures, hence cubic = 3 they are measured in square units, as they have only two dimensions.
No - because time is measured in seconds, not linear distance.
Yes they must be in the same units of measurements.
Conversion factor.