How much would it cost monthly to live in a small apartment?

As for me, in the summertime, it costs around $50 (water supply, cable, electricity, utilities). When it's winter, it's twice more - $100. The rent is about $500. Grocery is around $100.

Those are the costs of my life living in Ukraine. You living in Texas can have a completely different story, especially when it comes to groceries since you spend money depending on what food you prefer.

Depends entirely on where you live in Texas

The bigger cities it will be at least $1450

Smaller cities about $300 or $400 less

Rural areas about $500  to $600 less

$800 is a good estimate for rent for a small studio apartment. Add another $200 for utilities and another $100- 200 if you add groceries to it. 

That would depend on what such utilities charge in your area. Without knowing where this will be, no one can even guess.

Start calling the suppliers of such services in your area and ask THEM what they charge.

For instance, my cable/internet/home phone package costs me about $160 Canadian each month. My current electric bill is $61 Cdn. But, at this time of year, I have no need for air conditioning. Come summer, that bill will go up, while my heating bill will drop.

Groceries are both a matter of what supermarkets and deals are available where you are, and what you like to eat. So, go to a few and write down what an average buy for you would cost.

Really, you need to do your own homework.

All anyone here can do is guess. Most of those variables change by location which you failed to provide. The rest vary by user. 

FYI renting is not as simple as turning 18. Many landlords will not rent to young 1st time renters. Those that will typically require a larger deposit or a cosigner. 

It’s hard to get super specific without more information, because there’s a lot of variation in expenses. Air conditioning (electricity) is going to cost a lot more in Texas for a year than it will in Minnesota, for example. Grocery costs can be as cheap as a loaf of bread and jar of peanut butter each week to steak and lobster (and a whole lot of space in between).

As others have said, to qualify for an apartment on your own with rent of $800-850/month, you need to be earning at least 3x that gross pay each month. That basically translates to you working full time (40 hours a week every week) at about $15/hr. For the landlord, that requirement means that most people making that amount of money will be able to pay their taxes and their other bills and still have enough to pay rent (which should be the first priority bill you pay). 

From a rough estimate standpoint, you could figure $800 for rent and that much again for the other expenses you listed. You didn’t include any costs for things like transportation (car, insurance, gas, or public transportation costs), and those can be a couple hundred to a lot more (especially if you are making car payments and paying for car insurance as a young driver), so don’t forget to budget for that. Also, when you decide to rent your first place, you should get renters insurance. It can feel like a waste of money, but it’s pretty cheap, and if you have an issue, it’s totally worth it. You might not think you have much “stuff” or that it isn’t worth much, but if you had to replace everything you own you’d be shocked at how much it would cost to do so.

Few landlords will rent to 18yr olds, so the issue will be finding a landlord who will, the system landlord use is you have to earn x3 income to the rent you pay which means at $800 rent, you have to be earning $2400 per month and prove that, which enables you to afford to pay the rent, all the bills and can feed yourself as well

As a teen, it's extremely unlikely that you can afford your own apartment. Your income won't be high enough.

To start with to qualify for the apartment, the rent should be no more than about a third of your income.

You need to be looking at a room in a shared place.

Some apartments have certain utilities like water and sewer included. It's a lot easier to afford if you have a roommate. Groceries depends entirely on your diet and how willing you are to cook versus paying for ready to convenient food.