All that you described is normal, yes.

I would not introduce your dog and rabbit.  If you can keep them seperate, I think that would probably be the best idea. 

Your rabbit needs some time to settle into his new home. Don’t try to pick him up or bother him very much. Sit quietly next to him so he gets used to your presence, but don’t rush him into getting pets or held. He will come to you when he is ready. Since he is experiencing some level of stress, it’s normal for him to be eating/drinking less, and maybe not going to the bathroom as regularly. But it’s good he’s eating his veggies; just keep an eye on him, and expect for him to settle into a normal routine within a few days.

I wouldn’t introduce your dog, especially since you just got your rabbit. He needs to adjust to his new home and to you before he meets anything/anyone else. Keep his area clean, comfy, and quiet, and try to make friends with him gently.

Posted By DutchBunniesFtw on 01/16/2012 07:37 PM
!! HE JUST PEED AND ITS BLOODY / RED!!! SHOULD I BE WORRIED?!?! he peed on this dog bed i gave him and i didnt even notice until i took it out of his cage and it was light red. he got neutered on tuesday. is this normal? what should i do??!!?

Bunny urine can have a rusty color to it, that’s normal.  Are you certain it’s blood?
 

Red urine can be normal. What was the foster feeding him? Some veggies will cause the urine to change colors.

Otherwise, his behavior sounds completely normal.

What I did with my bun when I got her was I just sat on the floor and watched her, talked to her so she got used to my voice, and just let her come up to me on her own terms. I suggest that when you decide to pet him, pet him when it seems like he is asking politely for pets. He still may be very unsure right now, with it being only 3 hours. So when he comes up to you, just let him give you a sniff of your hand, if he runs, then he runs. But if he seems to stay, try giving him some soft pets. Do everything in teeny tiny baby steps. And always let him come to you, your relationship will be so much stronger in the end!

urine that is bloody usually isn’t colored fully, it would be like clots of blood in normal urine.

Red pee is normal. Read through a bunch of older threads in the forum here, theres tons of info about bunnies that you will find useful

Red urine is absolutely normal – it’s especially common after eating certain veggies like carrots or spinach. Some rabbits just tend to have more red in their urine than others even when they’re on the same diet. Like MB said, blood in the urine is more like clots, not an overall color.

The guideline for leaving a rabbit in their cage is in case they are afraid they can adjust. When Otto was a baby he didn’t want to come out at all so giving him time in his cage to just relax and settle in was good for him. When we got Hannah she was older and had a lot of energy, so keeping her locked up just made her more hyper. I let her run around for a bit from the very first day, though I kept a close eye on her because I didn’t know what she’d get into (compared to Otto who doesn’t get into anything). If you think he’s confident enough and really wants to be outside his cage, there’s no harm in letting him come and go as he pleases.

Just make sure he is coming and going on his own – picking him up right now isn’t going to build trust, so make sure he can get into and out of his cage on his own for playtime – you can use a treat to get him back in if you need to lock him up. Not wanting to be petted is also normal – he doesn’t know you yet and is probably more interested in exploring his new area than in being petted.