Yes evaporation can take place at any temparature.

Evaporation can take place because in the process it gathers heat from the surroundngs not from any particular source...

yes, as evaporation is a surface phenomenon viz. the molecules at the surface of liquid absorb heat energy from the surrounidngs or from the molecules of the liquid below the exposed part of the liquid and [after increasing their(molecules) kinetic energy and breaking free from the intermolecular forces of attraction] are able to convert into the gaseous state.