I'm a BIG fan of YNAB. I'll go through your requirements with it:
- multiple account (maybe multiple currency support) Yes - it lets you create multiple budgets, but it does not support multiple currencies in the same budget. You would have to either have separate budgets for different currencies, or convert all transactions to the same currency in the one budget.
- categories (shopping, rent, loan, car, school, entertainment, etc) Yes - you can have as many master and sub-categories as you want.
- synchronization between devices Yes - it syncs between mobile, tablet, and desktop apps seamlessly using Dropbox.
- useful graphs to know, where is possible to save money Yes - but only in the desktop app.
- app should be free or cheap No - it has a 30-day full-featured trial period for free, but after that you would need to pay to continue to use it unless you're a full time student (in which case you can get it for free if you send in your student ID). It is normally $60, but you can get it for cheaper by using someone's referral link ($6 off) or waiting around for their Steam sales (you can get it for 75% off, down to $15).
- easy to add new record Yes.
- etc..
You can import transactions from bank accounts, although I personally prefer manual entry immediately after purchase. YNAB is based on the envelope system. The forums and tutorial videos are a wealth of information, and the methodology is worth looking into even if you don't end up buying the app. The app license is for your whole household and uses an honesty system instead of limiting the amount of devices it can be installed on.
Oh - and other than being an extremely happy user and having a referral link, I don't have any connection to YNAB. I just love it that much, and recommend it to everyone because it changed my life!