I have a Bachelor's Degree in Electrical Engineering and my GPA is 2.6/4 (German scale, so it was like 2.9/4 in American GPA), mainly due to years of depressions and a bad break up. If I picked up work for a year or two in software development, is there a chance (and if it so, how far it is) to get accepted for a Master in Data Science in the US/Canada?
You will probably need to take the GRE and get a solid score. It also depends how you did in particular courses. E.g. did you bomb all the hard classes and ace a bunch of easy ones to pass overall? In grad school they may all be hard classes. Not to discourage you too much though. If you apply far and wide you may be able to get in somewhere with just about any background.
The concern of the school admissions is not just some competitive cutoff for merit, but that you will fail out and waste your time and money. There are definitely benefits of working, and it will help you. Especially if you get a job that uses some of the skills you need for your Master's program, like programming. If you can get a job precisely in "Data science" it may help significantly.
Yes. But, it will depend on you "building a case" that your GPA is not the important part of your story. Good letters of recommendation, good essays on the application, good test scores, etc. will help show that your GPA is not all there is to know about you.
Another good route to take (worked for me) is to take a grad-level course that would be a natural way to talk to a professor in the program. Do well, and you have another part of the story that you are not the same student that you were. AND, you may have a recommendation from a professor in that program (and potential advisor). The downside is that you are likely to have to shell out for that course, unless you can get your work to pay for it. (Check your employee benefits. I was a teacher, and continuing education was important enough that the district would help foot the cost for grad courses that were directly applicable.)
Don't focus too much on the metric of the GPA. It is only one of the ways that universities evaluate potential students.