Alrighty, I messed up my threads and didn't see this was priusdwelling...
So, a water boiler would be great, be it a $10 Amazon special with a thrift store pot, or a 12V ( truck stops have these) water boiling pot.
Use thermos cooking for pasta and such, a bit of thrift store time can yield some good, cheap, unused thermos's for cooking. Truck stops have a bunch of 12V small appliances...
PLEASE refer to the "Van Life" subreddits for advice on living in your car full-time. They can offer so much advice regarding staying warm and cooking in your vehicle.
My advice regarding your job, do not quit until you have another job lined up, as hard as that may be. You don't want to find yourself with an empty belly and a mind full of regret because you couldn't put up with your boss's bullshit a few more weeks. For finding work, try the app "Upshift"; You can pick up shifts through local businesses and get paid weekly. if an employer likes you and hires you on, you even get a $100 signing bonus. Amazon Flex, Uber, and Lyft are all also temporary (at least, I suggest temporary) fixes for money.
For food, I highly suggest cutting back to the value or dollar menu when you eat out; Wendy's has great salad options on their value menu. Use a cooler to keep lunch meats and cheeses (baloney and cheese if you have to budget the fuck out of yourself). You can get free ice and water by going through drive thrus and asking for a cup, or at most pay 25 to 50 cents. Do this once a day and BOOM, that cooler works just like a fridge. To cook food, I suggest this backpacking stove. https://www.amazon.com/Sahara-Sailor-Ultralight-Collapsible-Backpacking/dp/B014R1PAG6/ref=sr_1_10?ie=UTF8&qid=1532043545&sr=8-10&keywords=camping+stove+backpacking It's less than $10 and you can eat all of the ramen or canned, heated vegetables you'd like out of it. Fuel is cheap at Wal-Mart, around $6 a can (which if used sparingly can last you several months!!!) Make sure you pick up the correct kind. Any old pot from Goodwill on top will do (probably find one for $3 or less). I have the same stove and it has lasted over 2 years of abuse and use. Cooking in your car with the windows up is dangerous, so head over to parks or benches to cook meals. Side note, most all frozen, microwavable meal packs with veggies inside of them can be heated over stove top. Cheap, easy, yummy, healthy if planned right.
For showers and hygiene, get a $10 a month Planet Fitness membership. You can access the gym and shower 24/7, fill up your water bottles there, and twice a month they give out FREE pizza and bagels. I suggest buying a microfiber towel so you don't have to waste time waiting for a molding towel to dry. Laundry mats are self-spoken of, drive around to find the cheapest near you.
To park overnight, Wal-Mart never fails. Use your gut instinct to park away from the lights and not near to many other cars, yet not in a dark, sketchy area. Make sure you park at a 24-hour super-center. If you see an RV or Semi, even if somewhere states no overnight parking, you're in the clear. Just make sure you move your car around the next day to another spot! You have easy access to a bathroom all night and can brush your teeth here at night. Don't be afraid to park in other large shopping centers, car maintenance shops, ETC. Just make sure you move before the first employee comes into work to avoid trouble! You can also most certainly park your car in certain camp areas, just make sure you double check before doing so.
To stay warm, get a solid sleeping bag and fleece blankets. Always make sure you crack your windows a little bit. I know that sounds silly, but you need to make sure you have proper ventilation and the moisture inside doesn't freeze into ice! Fall asleep with a hot water bottle inside the "nest" of bedding. Don't be afraid to purchase a heated blanket for your car, these can run you as low as $25 if you look in the right area, but just make sure you don't run your car battery dead.
Give your new employer a friend's address you trust or a trusted family members. Maybe even a P.O. box? Also, note you can have anything you purchase online mailed directly to a Post Office near you and just pick it up that way, no charge. You may be near Amazon Lockers as well, not sure?
Use McDonald's, Panera Bread, Starbucks, local library, Crossroads Church, or Burger King for WiFi. Best to buy something to sip or munch on so you can stay as long as you can. If your car breaks down, don't fret to much. Get Triple AAA ($60 yearly, free roadside assistance to help you get your keys out of a locked car, they bring you enough gas to get you to a station, give you a jump, ETC.) as well as 4 free tows a year. Use one of those tows to get it to a shop, have the car appraised and given a time frame. Grab a motel for that many days. You can find coupons at Rest Areas if you drive along the highways near you for a little while, look for cheaper areas. Most likely run you $50 a night. Afterwards, pick up your car and resume life! If you're into an accident and it is totaled, yes, that causes a lot of issues, but so does if your house burns down in a fire; You'll make it through. Don't let this little statistical chance stop you from doing what you need!
If you're looking into being more one with nature, you seriously will love "Van Life". YouTube it as soon as you can. People have even converted their cars into tiny homes to travel and work at the same time, letting nothing hold them back, one being yours truly ;)!!! Honestly, best of luck to you.
P.S. Check out Devil's Head Lookout in CO, (It's free!). I'm planning on living out of my van up there for a while at the campsite come next Spring.
Seen some good comments, I'd like to add...
If pack weight isn't an issue, I highly recommend a portable burner. It's handy in a pinch. Here's the one I use. It's relatively inexpensive, and when you want to cook or boil water and can't/don't want to start a full fire.
When it comes to drinks, those single serving instant powder drinks (coffee, gatoraid, protein, iced tea) are great and can hide the taste of water purification tablets.
Also on the drink note, those those bladders are handy. I recommend filling one with everclear. It's versatile - in can disinfect a cut, start a fire, or mix with water and flavor powder to get you drunk!
Lastly, if you are set on a hatchet (I see a lot of naysayers) $30-$50 can get you something a little more versatile. Something like in the link offers a spade for digging, multi-purpose hatchet, and saw (which comes in handier than you would think).
Hope this helps...