Am I going to be able to get a good job one day if I only work part-time now that I'm 22, or do the employers want to see that I am working 24/7 (22 y/o male)?

Your current age and the fact you are working part-time is irrelevant when it comes to determining how an employer feels about the matter.

What is the best format to include a professional international assignment on a resume? (Engineering assignment in Japan for 6 months)

How you proceed is likely determined by whether your international assignment is part of your overall, i.e. additional experience, or your sole experience.

I would start off by taking a close look at what your duties in the assignment were. Cross-index them with the specific job description you worked under if you still have access.

Brainstorm a list of duties & skills that you were required to use in the position. Create a separate file with all of your brainstormed items.

My boss at my last job of many years is contractually forbidden to give me a reference for my job search, other than confirming my dates of service. How should I handle that in my resume and in interviews?

I see providing your boss as a reference for your current job searching as a wasted opportunity. If the new employer is checking you out, they are likely to contact your former boss anyways. And yes, they are limited to what they can say about you.

You would be far better off in creating better references. These are people that you have worked with. They may be work colleagues, customers, clients and/or other supervisors.

I have given six interviews so far and I’m constantly getting rejected in the final round. Why is it so?

Without ever having seen you in an interview situation, there is no way to answer this question.

But let’s turn it by a few degrees and look at it differently.

Every resume submitted should be based on the specifications in the job advertisement/description. Highlight your skills and experience so the interviewer can see that you are worthwhile interviewing.