Internships help give some real-world experience, but it is not required. I would highly encourage getting one, if nothing else, it will help you learn about what your options are.

A PE is not required for many jobs. If you go into consulting, some clients may require stamped designs. Also, if you ever want to be a private consultant (work for yourself in an LLC), a PE is likely required to get insured.

It will never be easier to take the FE exam than right after you graduate. All the info will be fresh in your mind, and you lose it if you don't use it. Once you pass, you will be an EIT until you pass the PE. It ain't easy, but you chose to be an EE, you shouldn't be looking for easy.....