I don't know who told you that "physics would get me nowhere, and that I'd [you] have to go after engineering if I really wanted to work". As far as I know, there are jobs available in physics, especially if you're looking to go into industry rather than academia. Although I think the job market...
In my opinion, hiding online status should still remain a privilege for gold members. However, it would be nice to get rid of the "Last seen" feature all together.
You aren't expected to choose which field of physics you'll work in right now. Since you enjoy physics, you probably should apply to universities with physics as your prospective major. Generally, you can take courses in physics/engineering and then decide which one you enjoy more. It usually...
There are numerous fields other than engineering where you can earn a lot of money, although that should certainly not be your main criteria for choosing a profession. I'd advise you to go with what you enjoy more.