1. You need either a fATPL or a MPL (a MPL is some sort of license which doesn't allow you to fly "small planes" after your studies until you reach a number of hours; you will only be certified to fly the planes of your company). A fATPL consists of PPL, CPL/ME/IR, MCC/JOC and your 14 ATPL exams.
2. It depends. Going modular will usually be the cheapest option. Cadet programs (usually MPLs) are often more expensive due to the fact that most airlines collaborate with expensive flight schools (L3, CAE, etc...).
3. Yes. You have cadet schemes who do support you financially. Take a look at the Lufthansa Flight School or the Wizz Air Pilot Academy.
4. Some airlines will pay for your type rating but you will be subject to a bond (leaving earlier = paying the difference).
Take this with a grain of salt, I am a "wannabe" myself.