Studio Apartment - 1600 PLN
Budget more like 2000 for something livable in a place where you have a fighting chance of not getting stabbed.
Transport - 110 (I plan to use a bicycle for travel though)
A monthly tram ticket and a couple of shortish taxi journeys per month will cost more than that.
Food - 500 (I cook on my own and have a little diet)
I really hope you like cabbage and hate both meat and dairy produce.
I'm also seeing no budget for personal care products or household cleaning products, please tell me that's an oversight.
Also, do you plan to wear clothes? You'll need a winter jacket at least every third winter and the same with boots. Those are 600zl a throw, so 400zl per year (more like 600 really), i.e. 30zl per month.
And do you plan to cut your own hair?
Health will be covered as per the labour regulations as far as the employee contract is involved.
Good luck using the state system without speaking fluent Polish. And even if you do, there's a very good reason a lot of people in Warsaw pay for private medical care.
There are lots of places here where 250zl gets you a round of drinks and maybe a tip for the barman.
the average salary in the city is 2,713 PLN. I guess people living in Warsaw are in huge debt.
Very few of those people live alone. And they all have support networks which you completely lack (you can't go home at the weekend and come back with your bags stuffed full of jars of food to get you through the week).