Because it is their duty to do so. actually all the brahmins,kshatriyas and the vaisyas who have had their upanayanam ( thread ceremony) must do their sandhya-vandanam and gayathri japa is a part of sandhya vandanam. the mantra is to motivate their minds in a positive manner so that they always yearn for the well being of all beings ( not just humans but all beings including animals,birds, trees etc) . this will lead to chitta suddhi - cleansing of the mind ( intellect) and that will make him worthy to try to achieve mokaha - liberation.

Gayatri Mantra is universal way of invoking positive energies to help keep intellect intact. There is no specific timing stipulations.

Actually most of they do not know, but some says " It kills Unwanted Bactaris & Gems , cerculating in Air "
But I can not confirm this say ji

Many do it as per their convenience.

Sandhya means the time in between day and night. It occurs twice daily once in the morning and once in the evening. It is traditional for Brahmins to pray during this time and perform Praatah Sandhya Vandanam and Saayam Sandhyaa Vandanam and invoke Goddess Gayatri by chanting the Gayathri Mantra.