Rabbit pee comes in a variety of colors, ranging from light yellow to reddish brown. Orange and red urine as a rule comes from carotenoids in the diet – it’s the same pigment that gives carrots their color. Many greens contain carotenoids that we can’t see because they’re green – this is the case with dandelion greens. Orange to red pee from plant carotenoids is completely normal. A rabbit can also sometimes spontaneously produce orange or red pee, and it’s still normal.

It’s wise to only feed carrot twice per week, but not because it colors the pee red. Carrots have a comparatively high sugar content, and rabbits shouldn’t have a lot of sugar in their diet.

Kale has a high calcium content. Some rabbits tolerate this very well, other rabbits don’t.

A rabbit that gets a lot of greens might not drink any water at all. It might get the water they need from the greens. It is however better for a rabbit’s health to eat more hay and less greens, because hay has a more rabbit-appropriate fiber-to calories-ratio than greens and vegetables. Rabbits need coarse fiber both for their teeth and their digestion.

All changes to a rabbit’s diet should preferably be made gradually. A rabbit who is used to a lot of kale and celery and carrot will likely eat too little hay if you make an abrupt switch. This can lead to serious GI-complications.

Darker poop as a rule means it contains more moisture.  You see it clearly in wild rabbit poop: During winter, their poop is dry and light in color, when the new spring grass starts growing, the poop changes to a darker color.

Please do not feed your rabbit entire carrots in a day — carrots are treats as Bam mentions, so at most, a thumb-sized portion of a carrot every couple days is much more healthy and appropriate for a rabbit’s overall diet: https://wabbitwiki.com/wiki/Treats

I wouldn’t be concerned about the presence of orange pee since, as Bam mentions, that is a normal consequence of some healthy rabbit foods. One of my rabbit pretty much only pees orange.

If your rabbit is eating a lot of veggies, they will be hydrating. That being said, you want to ensure your rabbit is eating an ample amount of hay each day since that is supposed to be the majority of your rabbit’s diet and its dry-nature is typically what draws a rabbit to drink water (e.g., rabbit spends a long time eating hay >> goes directly to water bowl to drink afterwards). I did not see you mention hay anywhere, so leaving this here for you to ensure you are providing a proper diet: https://binkybunny.com/infocategory/healthy-diet/

I agree with the others. That was WAY too much carrot to give. Not because it was turning your bunny’s pee orange (rabbit pee can be lots of colors), but because carrots have a lot of starch and it isn’t good for them to eat large quantities.

I would not be overly worried about your bunny not drinking a lot of water. Always provide it, of course. But sometimes bunnies don’t drink a lot because they are getting the moisture they need from their greens.