If you are an electrical engineer, will you be working independently or with a partner or group?

Sorry to be seemingly evasive, but really, "it depends". It depends on your assignment and the project you're on. But on average, companies and people in general are working on more and more amibitous and complicated projects. It stands to reason that more simple problems have already been solved or at least have a set of known solutions at the ready. With today's internet access, you can likely get a solution for just about any problem in any engineering discipline at all. That being said, people have a knack for raising the bar. That's the essence of free enterprise. To succeed, you have to do something better than the competition. Something cooler, faster, bigger, more efficient. So you'll generally be working with a team much of the time. Your own personal task may be an independent effort, but at some point, you'll most likely be delivering your results with the team. When you start out, you'll probably be given a mentor at the beginning stages of your career and maybe starting out in other positions. In general, you'll find all of these experiences will help you in your day to day tasks and you'll develop camaraderie along the way.

All 3 scenarios can happen on a daily basis. You should be ready for all cases unless you have your own company and your the only employee. Even in that case -- you need to work with other people to get your work done.

If you work for a small company then most likely you will spend some portion of your time working alone, doing circuit design, for example. However, most projects today entail working with groups of engineers, especially engineering projects at large corporations.

Electrical engineers usually work in a team, but they do sometimes work alone or with a single other person. They also work with scientists.