Nothing will happen if you touch your rabbit's urine, unless you have a skin reaction to rabbit urine, which is highly unlikely.
No, rabbit urine is not a carcinogen (cancer causing agent).
To effectively collect rabbit urine, you can use a clean container to catch the urine when the rabbit urinates. You can also try placing a special urine collection mat or tray in the rabbit's living area to make it easier to collect the urine. Make sure to clean the container regularly and store the urine in a cool place until you are ready to use it for testing or other purposes.
Is the bunny peeing somewhere unusual? Is she grunting/squeaking in pain when she pees? Is all the urine red or just a little bit? If you answer yes to those questions it would suggest the bunny has a urine infection. You need to take her to the vet ASAP! It is worth remembering however that of the bunny has had something with red colour in it, (Beetroot) etc. the urine produced can be a rather alarming red colour... A reddish rusty color to the urine could be normal if your bunny is not drinking enough water.
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If your rabbit is fat, it needs to lose weight. Obesity is very hard on a rabbit's organs, skeletal structure, and even skin (because an obese rabbit isn't able to properly groom itself, skin infections can result). Talk to your vet about how to safely reduce your rabbit's weight soon! The vet can also tell you whether or not the rabbit is pregnant. Orange urine is usually not a sign of anything wrong with rabbits. Rabbit urine naturally changes colour from clear, to pale yellow, to dark yellow, to bright orange, to darker rusty orange/red -- different reasons can include hormones, food they've eaten, mild dehydration, and even weather changes! If you aren't sure whether or not your rabbit's urine is normal, have your vet test it just to make sure. Blood coming out of a rabbit's genitalia is never normal and always a sign of illness or injury! If you think your rabbit is urinating blood, have her urinate on a white towel instead of her usual litter: if the red colour appears evenly spread throughout the urine, that's fine, it's not blood; but, if the red colour is in blotches, that is blood and your rabbit needs a vet as soon as possible! See the related links below for more details and helpful links!
This could be called colouration, the colour of urine, tinting, etc.. depending on your context.
A pink rabbit.
Rabbit urine can vary widely in colour from pale yellow, to orange, to bright orangey-red, to dark rusty red -- this is normal and natural. It's a simple internal reaction to the foods they're eating, how much water they're drinking, and/or hormone and stress levels. However, orange or red urine can also be a sign of blood in the urine. If your rabbit has bloody urine, it requires veterinary attention as soon as possible, from a special "rabbit-savvy" vet. Bloody urine could be caused by ovarian cancer, a serious infection, a kidney stone, an injury, or something else. If you aren't sure if your rabbit's orange urine is from blood, have it pee on a white towel. (Remove the litter from the litter box and put in the towel instead.) Wait for the towel to try. If the orange colour is spread evenly across where the pee soaked the towel, that means there's no blood. If the orange colour appears in spots on the towel, that's blood.
I would be guessing seeing as most urine is not good for your health, that rabbit urine is just the same. I would be very worried about your mental health if you are contemplating whether to drink rabbit urine or not. Please, do not DRINK!
To prevent your rabbit from spraying urine in the house, you can spay or neuter your rabbit, provide a suitable litter box, clean the litter box regularly, and ensure your rabbit has enough space and enrichment to prevent stress.