If you've ever done a CELTA, it's nothing like that. Also be yourself, that's the most important thing.
It really depends on how much you want to do. I was lucky in the sense that being introduced to the students I was, they have all continued to have lessons with me. An average week can be busy, but you never have to do more work than you want. It's important to remember that the students are flexible, but that means you have to be too. Sometimes there are some early mornings and late nights.
My biggest fear was that I had never lived in a foreign capital city before. I wondered if it would be too manic, but Budapest isn't like that. It's a beautiful place, and walking around it put my mind at ease very quickly.
You can, but you have to work for it, obviously. The wages are relatively low in Hungary so be prepared for that. But, the cost of living is definitely lower.
Paying tax can be a tough thing to sort out. One option is a KATA, which is basically when you are self-employed but pay a monthly flat rate (50,000Ft). This is usually a preferred option, as to employ someone in a company is very expensive for the employer.
Seriously, seek the help of a Hungarian person if you want help with this.