(this answer assumes the thickness of the plane is about 1 Earth radius, that is about 12,000km, according to the link HDE 226868 provided in the comments, there will be 9.81g everywhere, on either side of the plane)
Paradise for a few weeks.. then it gets perforated, again and again
So how would the sky look, at first..
Depends on the atmosphere the gods arranged for your infinite flat world. Suppose the weather will be stable, suppose some Earthly gods were involved in the creation and you'll have oxygen, water, blue sky and sunshine.
A week after creation (see calculation below) the inhabitants would notice their plane starts to warm up.. End of paradise will come soon..
Every 96 days, your sun will impact and perforate the plane
There are no stable orbits around the plane. Everything will fall.. When would the sun arrive ?

This formula works, until light speed is reached. Fillin the values, suppose the sun 1 AE away from you, that is 149,597,870,700 meters. If you multiply that by 9.81 your sun won't reach light speed.
So invert the formula, enter s = 1AE = 149,597,870,700 meters
in t square s / 0.5 g = 30,581,039,755, square root of that is 180,000 seconds, which is 48 days. Your sun will crash the plane and perforate it, proceeding its path through the plane and coming back again. After another 12 weeks, the sun will return and perforate your plane again, from the other side.
This can be prepared for, inhabitants could survive this: suppose your plane is infinite, the sun would arrive perpendicular, leave perpendicular and travel back through the same hole. Any place within 1AE of that point needs to be evacuated. Maybe it is advisable for the gods, to create a suitable hole in the plane, beforehand..
Blue shift
Your plane will now have a (local) "day night cycle" of 96 Earth days followed by a night of 96 Earth days, the sun oscillating through the plane.
Not only your sun, the whole sky accelerates toward you. This will cause the sky to be full of blue stars at night. Instead of red shift (expanding) your universe will show blue shift.
.. it goes into ultraviolet shift, your sky will get dark
When your plane has existed for a few months, the surrounding stars will start to approach with the speed of light. Remote stars and planets will reach your plane at light speed eventually, so you won't see them arriving. Their blue shift becomes an ultraviolet shift.
after that.. color oscillates, red-blue shifts alternate: purple skies ?
Disasters keep reoccurring, every few years the stars will return to your plane, perforating it.. and it will be quite difficult for the gods, to predict where these impacts will take place, to prepare holes for it. Suppose these gods are omnipotent, they could prepare holes in your plane for every star and black hole in your local galaxy..
The end..
After some 3 million years, the first neighbouring galaxies will start to collide.. and slowly, everything in the cosmos would come to rest on your plane. Oscillations would stop and every celestial object will come to rest in a hole, somewhere in your infinite plane. For black holes, these perforations will be giant. Light years of your plane will simply vanish. The inhabitants will have to move.. euuhm.. away from these perforations.
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NOTES about paths of light
I think locally emitted lights would not behave differently than light on earth, that is
Horizontal light rays travel horizontal until out of sight
Eventually, a horizontally directed light would reach the ground.. question is when and would that happen in sight ? I think not, with g=9.81 G the path of the light would not differ from Earth.
Vertical light rays travel very far away
There would not be any relevant effect. The light will travel against an infinite gravitational pullback and as Mike Serfas pointed out, the light will travel a trillion kilometers, until it comes to a standstill and fall back (?? I have to hand-waive this actually). But whatever happens, the distance is beyond any visible range, so the returning light will be so weak it can only be seen by Hubble.