3 month old kitty drinks then immediately pees

We picked up raja 5 days ago. It is worrying my wife and I how much he is drinking and urinating. Compared to my 4 year old siamese he's drinking/peeing about three times as much as her. He also has to pee almost everytime immediately after drinking. He did get vaccinated and neutered the day before we got him. I know that taking him to the vet will help more then posting our concerns online but we dont have the funds to do that for another week or two.

The other issue is that our 4 year old cat doesnt like him at all yet. However even though she is always pestering him, he doesnt react to her at all. Even if she hisses/lunges/swipes at him he just stares at her. His only defense is to stay perfectly still. When we put the 4 year old outside he then enjoys roaming the house, eating and filling the litter box with pee. Any helpful tips on him, his health and getting these two on the same page? Thanks for any and all help.

You need to take Raja to the vet to get him checked out for his peeing problem, the sooner the better.  

Here's an article to read.  

If you cannot afford a vet at the moment and you live in the US, please read this. 

If it were my cat I would be ringing around explaining his symptoms and asking if they will allow me to pay them in increments.  

You should definitely see the vet about the peeing and drinking a lot. It could be nothing or it could be something like diabetes, You can't know for sure without seeing the vet. They are usually really good about letting you pay later or set up a payment plan if you talk to them about it first. A lot of people find it hard to get the money together for the vet and they know that so they will help you how ever they can.

Cats often have trouble adapting to each other. There are a few things you can try to help them get along.
You can try playing with them in the same room. Don;t let them get too close to each other but let them see each other. Playing with a piece of string or something similar is a great way to get their attention off the other cat but having them in the same area will help them get used to each other. If they have separate toys try switching them around to. Give one cats fav toy to the other cat to play with for a while.

Another thing you can do is feed them close together. Maybe if you have a glass door somewhere in the house you could feed them either side of the door so they can see each other while eating.
Your 4yo needs to know that this new guy is not a threat to him. 
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Im sure there are many more tips that people have or some you could look up online. If you have never heard of Jackson Galaxy id recommend looking him up online. He has a tv show where he deals with this kind of thing all the time and i bet you could get some great tips from him.\

Best of luck to you.