I just got a new rabbit about 2 or 3 weeks ago from his previous owner, after about the first week I noticed he wasn't drinking, so I changed his water bottle to a bigger sized nozzle and he has been drinking very frequently especially at night, and he's been scratching the bottom of the cage at night, he does it occasionally throughout the day but not as frequently as he does at night. I noticed this morning that he started sneezing and he has been laying spread out on his stomach closer to the front, whereas he would usually lay towards the back where it is darker. After he sneezed for the 6 or 7th time I picked him up and sat on my bed with him and I noticed he was breathing very fast and loud compared to my other rabbit. I'm might just be overreacting but I've had rabbits before and never encountered this problem. I feed him Wild Harvest Advanced Nutrition Diet for Adult Rabbits, and I give him these mini rolls of timothy hay. I use Purina Tidy Cats cat litter the Glade tough odor solutions one, I just recently changed their litter because it was cheaper for me to buy it in a bigger size than by a 3 dollar bag and use it in one day. I use these for both of my rabbits and he is the only one showing alarming signals. My rabbits are different breeds, my female is a lionhead and the male, whom I am concerned about, is a giant sable mini lop.
You should try and get to the vet. What you are describing may or may not be a problem. As prey animals rabbits are very good at disguising sickness. I have rabbits in my home with similar issues as you describe. But I have also seen rabbits with similar issues suddenly stop doing well.
Even if you think the rabbit is going to be fine, you should go for a healthy visit within the first week or two. to establish a baseline with the vet if there is a future emergency.
Cat litter highly discouraged for rabbits. It can be dusty which is bad for their lungs, if they eat it can be bad for their digestion. Personally I prefer a wood pellet litter like this 40 pound bag that runs about $6 we also have post about rabbit litter What do I need to consider when buying litter for a rabbit?