What would be the monthly costs of living by myself ?

I suggest building a budget; include all income and expenses. Typical monthly expenses include: Rent, Water, Cable, Internet, Phone, Electricity, Car Insurance, Groceries, Gasoline, and Cash (spending money). If you don't have enough money coming in to cover these expenses, consider getting a roommate.

Make a savings plan to prepare for moving out. There are lots of "start-up" expenses involved in moving out the first time: Deposits for apartment and all bills, Furniture: bed, couch/chairs, coffee/side tables, tv stand, TV, Computer, Microwave, Pots & pans, Dishware, Silverware,Bedding, Toiletries (towels, shower curtain), and the list goes on. Buy what you can in preparation for moving to decrease the amount you're spending at one time.

In addition to saving for the items listed above, put some in savings for a “rainy day”. $1,000 is the minimum, 3-6 months bills is recommended.

No way to know. YOUR living costs depend on YOU. Might be $1000 per month, might be $10,000 per month. No one here knows your income, lifestyle, or spending habits.