My planet is Earth like in size (I can change it, if needed), however its day-night cycle is somewhere around 1,000 Earth days long. How hot would day get, and how cold would night get? Is it possible to have plants and animals on this planet? Oh, it also has around the same amount of ocean as Earth, yet again, can be changed if needed.
-120 to +102 degrees C
You've used "Earth-like" so I'm assuming everything else is Earth-like too, with the only difference being the slight counter-rotation allowing a day to be 3 times longer than a year.
So I can answer this by building on this detailed breakdown of an Earth-like planets weather where the rotation was 0, but the planet still went around the sun, giving a year-long day - ie it was calculated for a world with 6 months of sun followed by 6 months of night. Yours will be about 3 times more intense, you have 500 day nights and 500 day days. The "midday" storms will move about 1/3rd the speed across the surface but will keep the basketball sized hail. You'll get the strong winds at dusk blowing everything away. You'll get carbon dioxide falling at night. And you'll get the devastating floods and Earthquakes at Dawn. Plus everything else detailed in that link.
The same maximum temperature (102 degrees C) will be hit in both cases, however your planet will get a little colder than the one in that maths. Exactly how much colder is hard to estimate but a few extra degrees colder (to about -120) seems reasonable.
On average, a little bit colder than Earth.
But that's on average. The dayside will be really hot, the nightside will be really cold. The average a bit cooler because the increase in radiant heat loss on the hot side will be greater than the reduction of radiant heat loss on the cool side.
Actually, don't think of it as a "day" and "night" side.
Rather think of it as "500 day long sunless winter", followed by "500 day long summer with no nights"
Fortunately, the atmosphere will do a lot to help distribute the temperatures. Expect wind. A LOT of wind. Very disorganized wind, likely channeled by surface topographic features, because there is almost no planetary rotation to induce coriolis-powered rotation. So despite the plenty of wind, don't go looking for rotating storm systems. No traditional hurricanes for you, sorry.
So I expect the locals talking weather would be like:
In the morning the wind blows off the glacier down this here canyon as the CryoSnow (dry ice snow) evaporates. It's still a bit chill then, of course, but you can shuck the EVA suit, you should need only the heavy parka. Gotta remember to wear your mask. A couple weeks later the winds will turn, blow back down. This time its a hot, dry wind coming from HighSun. That's when we expect the spring floods. No, not from the winds, you silly! From the glacier. Then there's growing season. We got's to pop out four crops of corn before it gets too dry. By HighSun everyone is in the shelter, of course. Its quiet, and dry, and ... did I mention not to leave your tools outside? At least not until the clouds come back. That should be a week or five after HighSun. Not that they ever bring rain, mind you, its just warm, and steady wind. This is when we rebuild shelters, and enjoy the outdoors as much as we can.
For remember: The winter is coming! A week or two before sunset the winds build up, cover the sky with clouds and bring the Darkness. You will never see a sunset, the dark skies will just gradually become the Dark, then the DARK.
Around day 50 the Dark becomes the Cold, and it starts snowing. No more, no less than 73 meters of HydroSnow. Remember to charge your shelter's air supply before this!
Around day 250-300 of the Dark it starts snowing again, this time its the fluffy CryoSnow. Not so much of that though, 5m of dry ice is a heavy fall.
And then you just wait for the summer to rise again
Personal P.S. I strongly suspect the dominant Religion will be: Cursing the blighters that thought colonizing this excrescence of a planet was a good idea!!