4 weeks old. first time orphaning a kitten

Here I am at one in the morning hoping to get advice..
I know you all hear a million and one kitten stories and if like your input and advice on mine..

A little over a week ago, this kitten came in to my life by surprise. She was given to a little girl at my nephews boys and girls club.. obviously she couldn't take care of it. So my nephews mother brought it home, and was going to give it cows milk.. I researched right away I found that was wrong. Went straight to the petstore and got her replacement milk.. she was week when she arrived now is climbing and pouncing everywhere.. I'm guessing around 4 weeks old.. she's off the bottle now and is drinking the milk from a shallow bowl.. everyone and a while I sneak in some soft food in with the milk.. she eats some, but not enough as I'd like.. but I know with in time.. now I'll be moving back home and taking the kitten with me.. but I do have questions for all you readers.. as this seems to be the best forum I've come across... her tummy is plump.. forgive me I forgot the proper word.. from What i read it is or most likely is worms.. my question to you all is.. should she be dewormed now or is she to young? When do her shots come? BTW her social skills seem good, she loves to play eat and sleep.. must be rough as a kitten. She doesn't drink water, is that Okay? If you have any questions feel free to ask. Thanks again
P.s. her names zion

Most vets will deworm kittens that young if it's clear that they have worms, and it sounds like she does. Otherwise, the first dewormer is usually given around weeks 6-8 (though it varies based on the vet). The same variation happens with vaccines. The FVRCP vaccine is the most common, given as a series of three shots spaced 4 weeks apart. 

Usually when I have fosters they go in at 8 weeks and are dewormed and given their first shot. Then, at 10 weeks they go back and are spayed/neutered, microchipped (best to do it then since they are already under), and given the second dewormer. (Note: Kittens can be altered as soon as they are 8 weeks and at least 2 pounds, though most don't reach 2 pounds until closer to 10 weeks which is why that age is the most common for altering). At 12 weeks they get vaccine #2, and the final one at 16 weeks. At this final appointment some choose to give the rabies vaccine (if required by law where you live) but I like to wait and do it as a separate appointment. Sometimes vaccines can make cats sick and I don't like to give more than one at once. 

I would encourage you to do your research on what vaccines you want to give her. Most people don't have an issue with the standard FVRCP series in kittens, but there is a lot of controversy about whether there is any benefit to further vaccination. For example the FIV/FeLV vaccine will always make your cat test positive for the disease, meaning you never actually know if they have it or not. IMO, this vaccine should only be given to cats at an extremely high risk of exposure (i.e. ones that live with other FIV/FeLV + cats or if they are feral). Because I foster I keep my two UTD on their FVRCP and rabies as required by law but do not give any other vaccinations. Do your research and find what fits with your beliefs and your lifestyle. 

So, As soon as you are able I would find a vet for her and get her in for her appointment. You can deworm her then and talk to your vet about setting up her vaccination and spay schedule. They all do it a little different so if your vet says one or two weeks in either direction that is nothing to be concerned about. However, I would not put off spaying past 16 weeks of age. At that point she can come into heat which not only makes her susceptible for unwanted pregnancy but makes her spay more complicated. They tend to bounce back quickly when they are young so just get it over with!

To answer some of your other questions: while she's still primarily on milk she won't drink water and that's okay. Keep adding wet food to her milk and increase the amount each day so she gets used to it. Also, make sure you keep fresh water and dry food out for her at all times. It may still be a few weeks but she will start to explore these and they need to be available. You also need to start getting set up to litterbox train her if you haven't already. A high sided cookie sheet works well for a kitten box. Be sure you only use non-clumping litter at first as clumping litter can cause a life threatening blockage if ingested. Check out the threads in the pregnant cats and kitten section for a lot more information on what is to come! 

My only question to you would be how will you travel back home? If by car then that's no problem just make sure you have a carrier for her, but if you plan on flying be sure to check with the airline. Most have strict rules about flying with pets and that they must be UTD on their vaccines. If that's the case you need to talk with them about exceptions for hand reared animals under 8 weeks. You may be able to get away with it so long as you carry her on (which is what you should do anyway). Just something to think about as you make your preparations! 

Thank you for taking this little girl in. She is very lucky that she made her way home to you! Ask more questions if you have them, and welcome to TCS!