I agree with you on the professionalism- I'm big on first impressions and a CL/resume may be your first with some companies. Looks like it will be with Spirit since we've never been a big presence at job fairs.

As for the contact name, I'd recommend addressing it to "Spirit Airlines Pilot Recruiting Team" or something very similar. We don't know who will be on the panel, but it will assuredly be more than one person and this title will suffice. I'd use the aforementioned address (2800 Executive Way).

As for the copy/paste of a cover letter and resume, I'd suggest you combine them into one word document and just ensure they are page 1/page 2; that way they will view them both. Others would argue that the website is only requesting a resume, so that's all you should submit. I don't believe in Jedi mind tricks, so I don't think this is a sticking point. Do whichever you are more comfortable with.

Hope this is what you're looking for and good luck!