Q: What is the rule of dimensionless quantity?

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Yes. Conversion factors will generally be dimensionless constants.

Yes, the magnitude of a vector is a scalar.

Relative value is a dimensionless quantity, and so it shouldn't matter what units you want to use, as long as you are consistent.

Correct: it is a dimensionless number.

A dimensionless number has no units. The units of all variables that compose the dimensionless number (product or ratio) must cancel each other.

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If a quantity is "dimensionless", that means it has no units, and it's just a number.

energy/mass example: calories/gram

No, a dimensionless quantity does not have a unit because it represents a pure number without any physical dimension. Examples of dimensionless quantities include ratios, proportions, and mathematical constants.

the dimensionless numbers have the definition as that of dimensionless groups, and have all the properties which dimensionless groups have.

No. "Dimensionless" means there are NO units involved.

Yes. Conversion factors will generally be dimensionless constants.

No, a quantity cannot have units and still be dimensionless. The dimensions of a quantity are determined by its units, so if a quantity has units, it has dimensions. Dimensionless quantities are those without any units.

Yes, the magnitude of a vector is a scalar.

Strain is dimensionless quantity because strain is the ratio of the same quantities like change in length/original length,,change in volume/original volume. e.g tensile strain=(change in length)/(original length)=m/m (S.I unit) so its a dimensionless quantity.

The coefficient of friction is a unitless value because it represents a ratio of the force required to move an object over a surface to the weight of the object. Since it is a ratio of two forces, it does not have any units associated with it.

Yes, a quantity can have units but still be dimensionless if the units cancel out when they are raised to the power of 0. For example, specific volume (volume per mass) has units of m^3/kg, but when you divide volume by mass, the units cancel out and it becomes dimensionless.

The coefficient of friction is dimensionless; it has no units.