For item 1, basically, EOI only requires 'suitable skills assessment' notice to claim points for your 'education' - so Teacher registration is not a requirement to submit your EOI.
Item 2: Do you mean you submitted your PTE-A for AITSL assessment? - Basically, AITSL (which is required for EOI application) ONLY accepts IELTS. While you can use your PTE-A for EOI submission.
Item 3: You may want to check Victorian Institute of Teaching website for the requirements. But basically, if you have the qualifications e.g four year (full-time or equivalent) teaching qualification undertaken at a higher education institution; you may commence your application for "Teacher Registration". So initially you may be given partial or provisional or full registration, ALL depends on your qualifications.
I am confident that you are aware of how lengthy and challenging it is to be 'registered' in a state as they require standards such as:
you must demonstrate that your professional practice meets the Australian Professional Standards for Teachers (APST) at the proficient level, and
Nationally Coordinated Criminal History Check (NCCHC)
In short, you need to be working in Australia (such as Victoria) to even start with the application for registration.
Item 4: You may want to check with a migration agent as they are most familiar with the requirements of each state depending on the visa you are applying for (e.g. VIC requires ACECQA certification for ECE V190 applicants). I can't say which is most offshore friendly but my agent shared the following for ECE V190 (which may give you an idea how is it now. However, "you can still very well apply EOI even if that occupation is closed":
NT is closed
ACT Canberra Matrix is closed to overseas applicants
SA available to international graduates
TAS available to international graduates
NSW ONLY selected health, ICT and engineering occupations
