Most of your questions are answered in detail here: http://sloperama.com/advice/
but I'll add a few things as well.
First off, you absolutely do not need to be a programmer to become a game designer. Game design consists almost entirely of writing and math. Game programmers are hired to program games, and you don't have to have working game demos in order to break into the game industry. Focus on writing, math, and understanding what makes games fun, rather than trying to be a jack of all trades with the programming -- modern game development involves very specialized professionals, not jacks of all trades.
You will definitely need a Bachelor's degree though. Unfortunately your Associate's degree doesn't count for much -- I've been in the game industry many years, and I've yet to meet or hear of anyone with an Associate's or even a Bachelor's in Game Design who is working as a game designer now. If you're almost finished with your Associate's, go ahead and finish that, then start working on a Bachelor's degree. Otherwise you might want to consider moving directly onto a Bachelor's degree.
The good news is that you can get your Bachelor's in anything you want. Try to graduate as quickly as you can so that you can start working (years working in the industry will count for more than years spent in school), so if there is a Bachelor's degree that your Associate's will count towards, do that. Along with your major take math up through Calculus 1, and at least two courses in Statistics, two courses in writing, one Computer Science course, and one art course. Math and writing are the main tools of a designer, and the CS and art courses will help you work with your programmer and artist colleagues later on. Fill up the rest of your course requirement with a wide liberal arts education -- history, literature, mythology, sociology, psychology, etc, are all useful in game design.
You should also be playing a ton of games, and taking notes on what you liked, what you didn't like, and what specifically you would change. Try to be as specific and detail oriented as you can -- there's a lot of refinement in design, sometimes as small as changing damage from 35 to 32, or moving one word in a sentence. This will help you start to understand what makes a game fun, and will train you to pay attention to the details.
Once you have your Bachelor's degree, you'll need to realize that almost no one is hired to be a game designer as their first job in the game industry, and there are almost no game design internships. If you see a job posting for an entry-level/junior designer position that requires no previous experience, definitely apply, but those are few and far between. Most game designers start out in Quality Assurance or customer service, and work their way up to design from within the company. Nearly all game companies post job openings internally before they post them publicly, so people working in QA, etc, have first shot at an opening for a junior design position.
All the way up through getting a job in QA or customer service, continue to develop your design skills by taking notes on games you play (including games you test for work -- but on your own time, not the company's time) about the specific design changes you would make. Write up your own design documents about your game ideas, and again be as detailed as possible. But focus on getting a Bachelor's degree and getting hired in any capacity at a game studio, while developing your design skills, rather than trying to become a programmer as well.
FWIW, my very first job in the game industry was working in the mail room of a well known game studio (you would recognize the name). I eventually worked my way up through office support to customer service. After a couple of years of customer service, I asked the Lead Designer what I would need to do to move onto the design team. He asked me to write up a design document on what I would do with the newest game concept the design team was working on. I did that, and several months passed. Then I was told they didn't have an opening on the design team, but they needed a junior producer. I worked as a producer for about six months, and then was thrilled to find out that a spot on the design team had opened. Because the team knew me and trusted me, and because of my original design doc almost a year earlier, I got the job without it ever being posted publicly. The road to becoming a game designer is never straight, nor smooth.