1. Converting a non EU ATPL is going to become more difficult. Italian Civilavia is still not in line with JAR-FCL so your best bet is convert your licence via the UK. You could get a validation on your current licence but you'll need an airline to sponsor you for that. This will require something like a B737 rating, with experience on type to justify an airline entertaining you with a foreign licence.
2. Who opertaes B737s? Blue Panorama, Air One, NJI and a series of new start-ups.
3. Salary can be between 1.8m-7m lira per month after tax. This depends who you work for. Volare is at the low end and Azzurra-Meridiana and the high end of the salary scale.
4. Best airline to work for is probably Meridiana. With 40 hrs flying a month you take home around 6.5m lira and you have at least 12 days off per month.
Good Luck!