Mercury grand marquis whistle sound light dimming

When I drive the car sometimes I can hear a very
high pitched whistle sound, and when I use
electronics light the button that rolls the window
down Or turn on the radio etc. the lights slightly dim
for a second until I let go of the button, they only
dim when using electronics when the cars making
that sound. I believe it could be a loose connection
on  the battery but I’m not certain, need help, thank
you