A folded antenna is a dipole type.

A full-wave loop antenna can be interchanged with a folded dipole without much difference. The input impedance is similar and the only difference is in the directivity: a full wave loop radiates along the axis of the loop, while a vertical folded dipole is omnidirectional.

I don't think it has. Bandwidth depends on the diameter to length ratio of the antenna. The greater the diameter of the elements the wider the bandwidth. The inductance goes down and the capacitance goes up, giving the antenna a lower Q. the folded dipole has a greater effective diameter (at least double for the same materials). You can increase a normal dipole's bandwidth by increasing the diameter, hence the old time birdcage aerials.

The Yagi array allows a significant increase in antenna gain (expressed in dBi or Db over isotropic) by the simple addition of parasitic elements to a dipole or folded dipole.

The impedance of a centre fed dipole at resonance is about 73 ohms. The feed impedance of a folded dipole is four times that, 292 ohms. The feedpoint is of course balanced in both cases, thus 300 ohm balanced line is an excellent match for the folded dipole active element of a commercial TV antenna.