Hi velua,
I was able to do a summer internship even though I had already graduated and was planning to take a year off. For my company, they were okay with it even though I said I was planning to attend grad school the following year. I would imagine you would be in an even better position than I was since you are still taking classes (although as a non-degree student), since it's some sort of evidence that you will be continuing your education.
As for research, I don't know what the norm is, but I was able to do research even though I wasn't a student anymore (I finished my degree early). I think professors would understand since research experience would be a large part of the graduate application.