You can't get hired if you don't apply. They'll flush out your skills in the interview and, if they hire you, they'll find a place where you can use the skills you have (and learn more!). I landed an internship after my data structures course.

The most important thing to remember is you can't be hired if you don't apply. I'm a freshman in university now and had my internship between Junior and Senior year of HS, and I certainly wasn't qualified for it when I started, though the hiring company seemed to disagree ;) Having the audacity to ask was what got me that job, and it has lead to plenty of opportunities since.

To get back to your question, the answer is "it depends". Is the team you're going to be working on essentially looking for a new employee they'd like to hire post-graduation and have around in the meantime, or are you going to be applying for an internship at a larger company where they might not be focused on coding prowess so much as "smart" and trainable? Either will figure out during the interview process whether or not you're a good fit, and find a place for you to use the skills you have and learn new ones.

It depends on the place. Some places are willing to train you if you have a decent fundamental understanding of programming concepts. They'll probably see this by asking you to write a sort, a recursive function, a tree or something like. Other places may expect you to have prior knowledge. The thing is always to start early with your job search. Apply to work study jobs if you really can't find anything. It won't be as stressful and you'll be able to get some programming experience in. Pursuing in side projects will also help you gain more programming experience / it'll be something you can use on the interview.

It's not your job to decide if you are competent enough to be an asset to the team, it is the company's job. If you want the internship, apply. Let them do the work of figuring out if they want you.