Canada

You can do a MS. You must see that your B.Tech grades are more than 75% to be considered. Take GRE and IELTS. Since Germany is extremely competitive I am suggesting you GRE or GATE, Canadian universities are also very selective, check the university websites for GRE requirement. Not all of them requires a GRE score. Practically speaking entry requirements are different so please visit the university websites for details.

For MBA courses, you can try looking at these options.
Memorial University of Newfoundland,
University Canada West,
Universit de Sherbrooke,
Trinity Western University.
There are other universities which offer Masters of science in management courses. Those are similar to MBA but different in course structure. If you are open to that course, then you will have a lot more options of universities within your budget.

Most business schools will ask for GMAT+ TOEFL/IELTS scores as admission criteria.You must check the school website to make sure you prepare accordingly.

Yes, please appear for GRE and TOEFL. c

No, you need to appear for GRE.

It is possible, if your wife has applied for a Canadian fulltime study course with proof showing eligibility of having funds for the stay and the tuition fees of the course, also then you can apply for a Canadian student visa.

Scope is good, MS Management programs are meant for students with limited or no work experience. So, you cannot expect to land up with a higher management role immediately. Having said that, prospects are really good and employer do look for fresh graduates ready to adapt, with flexibility and zeal to learn. London is difficult with stiff work permit options for international students. Canada is more preferred now due to the post study work options.
Best Wishes.

McGill, University of Alberta, Queen's University, University of British Columbia, University of Toronto, Western University are few of Canada's popular B-Schools in terms of reputation and career outcomes.