EIRP and ERP

Effective radiated power is the power supplied to an antenna multiplied by the gain of that antenna compared to some standard antenna. Unqualified, it is usually taken to refer to the gain over a half wave dipole, but it doesn't have to be, it should really be stated.

Effective isotropic radiated power is just effective radiated power referred to a theoretical isotropic radiator, which radiates equally in all directions. Such a device does not physically exist, but is nevertheless useful in theoretical field calculations.

Effective radiated power is usually taken to mean ERP in the direction of maximum radiation for the antenna under consideration.

A dipole antenna which is electrically one half wave long, in free space, exhibits a gain in its direction of maximum radiation of 2.15dB over a theoretical isotropic radiator.

Somebody at some time will have made field measurements to derive the antenna's polar pattern, hence its gain, but ERP is usually just derived from input power and antenna manufacturers' gain figures.

From antenna gain, radiated power and the inverse square law, hence power density (watts per square meter), and the intrinsic impedance of free space (120 * pi, about 277 ohms))

Correct

No, EIRP = (power to feeder) *times* feeder loss *times* (antenna gain over isotropic).