What are my chances of of landing internships and competing with younger applicants.?
First of all, good for you !!!! Education later on in life is a huge accomplishment and in my view, shows you to be proactive and in charge of your career. I don't know your background but I value the experience someone brings to the table, not necessarily the initials after their name. All forms of education make someone marketable regardless of when it was achieved.
I would highlight your achievements, any volunteer work you might do/ have done, the value of your network and wisdom. I would hope employers see past the date of graduation.
I can't be real certain on this question. I would advise you to explore companies offering the internship and call them if you have concerns. I experienced very few internship while i was attending college, however now that i have completed i see more opportunities. As we know age discrimination is not to be occuring.