Yes they must be in the same units of measurements.
No, it is not true.
No. Measurement units are defined by and conversely. So the same units necessarily means same dimensions.
Same direction and equal magnitudes.
The answer will depend on (a) whet the dimensions of the two quantities are, and (b) what the missing operator between the two quantities is.
Yes, always. One molecule plus one atom is not 2 of anything. One unit north plus one unit east is not 2 units northeast. ■
Scaling is when you multiply or divide two quantities by the same number.
Certainly. [Speed] may have units of feet per second, kilometers per hour, or furlongs per fortnight.
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.