Hi Alina,
I’m no expert on the tax question but i think you have to earn more than 12,000 (not too sure about the exact amount) before you are liable to pay tax. For a very rough estimate 25-30% of your gross salary goes to pay taxes and social security and the remaining 70-75% goes into your pocket. The cost of renting in Madrid can vary a lot, i think if you want to live on your own then the cheapest rental will be about 600 euro per month for a studio apartment in the city centre. Further out of the centre will be considerably cheaper. If you rent a room (shared apartment) you will pay perhaps 300 euro per month. In either case you will have to pay bills on top.
I hope this helps, i live in Madrid so if you need any help please drop me a note, i can even put you in touch with a Romanian girl i know if you wish.
Good luck,
Ranpal