Dear mage,
Kudos to you on thinking about your application so far in advance of your application! You ask many good questions; see my responses below:
1) Stanford and Harvard do not exclude applicants based on age. You will be a little older than their average age, but definitely in the range of the majority of a typical MBA class (24-30). Your profile appears to be a solid platform so your GMAT score will definitely give you an idea of how competitive you will be for top programs. You should target the 700s for top 20 and 650 or higher for top 40 programs.
2) In addition to a high GMAT score, you will want to gain some leadership or project management experience in your extracurricular activities if you can. This is more important if you have limited leadership in your professional experience. Perhaps there is a nonprofit you can work with or a leadership role in a salsa club?
3) Internship experience does not count in your years of work experience but is important to your profile. "Years of work experience" as reported in class profile statistics is only post-bachelor's degree, professional experience.
4) In terms of US schools, you will stand out because you are from Greece and have US work experience (both positive). I think your experience with the Olympics is also interesting. You are correct that your engineering background and work experience will be quite common, so find examples that might be unique or professional responsibilities you had earlier in your career than others.
5) It is best to have one of the professional services do a GPA translation for you. They can also translate your transcript from Greece if it is not in English.
6) Yes, being a PR does make a difference for both admissions and career placement. Since most schools keep their international population to 25-40% of the class and their applicant pools can be over 50% international, it can be harder to gain admission as an international applicant. However, if you have a green card application in process at the time of your application, you might be considered in the US citizen/PR pool but will want to check with the schools you apply to for clarification.
Best of luck,
Lisa