1. No,this is not true.
2. Electronegativity is the ability of an element to pull the electrons of another elements towards itself in an chemical bond.
Electron gain enthalpy on the other end is the energy released when an element gains an extra electron in it's shell.
3. It is not necessary that element that have high electronegativity will have high electron gain enthalpy. This is because, Fluorine has very high electronegativity, but it's electron gain enthalpy is lower than Cl (which has low electronegativity). This happens because the size of F is small, and the 7 electron repel the incoming electrons.