Specific openings change a bit throughout the year but generally, yes, you can. We often have openings for candidates without much experience as long as they are TEFL certified. We also have programs to combine TEFL training with job placement.
If you're asking for Korea specifically, the positions we have available have a pretty narrow salary range regardless of experience and qualifications - Pay is from 2mm - 2.8mm Won per month ($1,800 - $2,500 USD) and you could probably expect to be in middle-high end. In China, you could expect $2,300 - $3,000 USD/month.
Depends on which country you're moving to. For example, some cities in China require your pet goes into quarantine for a couple weeks upon arrival, while other cities do not. Long story short, it will add some challenge and probably some cost but it's definitely do-able.
Generally speaking, only candidates from recognized native English speaking countries are eligible for this program.