IELTS

Yes, good enough for New Zealand. All the best.

Not a very popular choice for MBA but you can look for universities under G30, they offer programs in English. You will require work experience and all applicants are required to submit their scores for GMAT or GRE. An IELTS of more than 6.5 will be required. Please check the university websites for money matters but most Masters Programs typically range from Yen 665,676 - 1,229,631 per year . As far as PR is concerned you must live in Japan for more than ten years or so with an employer-sponsored work visa.

Oxford University also accepts IELTS score. I suggest you to appear for IELTS test only; TOEFL score will not be accepted for UK Visa.

You need to know that admissions are granted on the basis of academic grades and not alone on IELTS and PTE scores. You must mention your education background and how much you scored for precise information.
Secondly, the IELTS core of 5 is not accepted anywhere. A score of 6.5 above is required. For PTE scores 54 is decent but check for every entry requirement on an university website.

Yes, but those are useless. So, you just concentrate to raise your marks.

Kindly mention your desired engineering branch and the country you are interested to study at.

You can buy Cambridge part 11 and do the practice tests or you can analyse your score if it is in the bracket of 7-9, then you need nothing else.