There are many physics students who go on to graduate school in engineering without any undergraduate engineering experience. It’s very common and almost certainly a better option than getting a second BS in engineering. To answer your other questions:
- Your GPA is a tad low but not so much so that it kills your chances. Do you have any research experience as an undergraduate? That would help you out in that department.
- Most likely you would have to take a few classes to get you up to speed with whichever program you choose to pursue. With a physics background, ou are already fairly well-equipped to handle most engineering classes but there will likely be a couple of foundational courses in your area of interest that you are encouraged to take.
- The career services at your university can likely help. Otherwise you may have to start browsing company websites for internship opportunities.
- Do you have an engineering field in mind? What about a research area? I'd give some thought to that and try to get some research experience on your current campus of you can.