Regarding designers:
What technical abilities do game designers tend to cover and how does it tie into their work? How much of a technical focus, should a designer have in terms of art and programming?
Regarding work process:
Is there a conceptual process where designers prototype digital games? What tools can be used in this process?
How can I start my digital projects? Is there a good guide for this, generally?
You need to make a distincion between big projects / teams / studios and small Idie devs.
If you are working on your own, or in a small Team where everyone needs to wear multiple heads, Game Designers will most probably also be artists or programmers. Some work with freelancers, but when you have to outsource art AND code, it might get very expensive to do even a simple prototype.
So it is highly advisable to get competent in at least one of these skillsets, so you do some concept and prototype work on your own besides just writing a GDD and designing the game logic.
Also, given you seem to be very new to the topic, you will most probably HAVE TO work on some hobby projects before you can hope to enter the industry, even if you plan to get employed by a big AAA studio (and let me tell you, Game Designer is NOT a junior position). Even if you go to a Game Design school, adn you get a degree, without a very good portfolio of your own work (school projects alone will most probably not be enough), and a realistic entry level job skillset, like level design (which in turn will need some art, and some coding skills), you will have difficulties finding employment.
What you should do:
1) Follow your passion. Do you REALLY want to create games? If yes, why are you not doing it right now? Is it only because you are confused, or do you just not like the process of creating games (which for everyone besides the high level devs means getting their hands dirty on code or art, and for a lucky few who are able to work as game designers in a non-lead role getting their hands dirty in excel).
2) If you really are serious about game development, think what you want to achieve. Do you really want to reach a game designer position? Even if that is a longterm goal that might mean you need to do others things while you work your ass off to impress your bosses?
Do your want to work for an AAA Studio or do your own things? Indie Development is not an easy way to get rich, and just as hard to survive on as landing a job with your AAA dev studio of choice. Do your really want to go that route?
3) Learn practical skills. Make yourself useful in a team. Above all, accept that IDEAS are NOT worth a dime in this industry, unless you have a name to go with it (if John Carmack has an idea, it is worth millions to some investors. At least it is, if he also uses his skills to pitch that idea to said investors the right way).
Try to learn coding. If you want to produce your own prototypes or games, you will need code. There is no substitute. You can create a game without any art skill as long as you can code (by using either ugly programmer art, placeholder art or byuing stock art).
If that fails, become an artist. Get good at it. And see if there is a team looking for an artist you could work with.
4) If you want to go the extra mile to get a degree once you know game development REALLY is your thing, be VERY careful which school you pick. There are many bad schools out there that do game design courses.
Below are several game ideas I would like to test digitally.
I just want to develop the skill set to make the first one by myself, in something like flash. But i'm not sure whether it being flash matters or not.
I'm basing this off of a game I saw, which is also a flash game. I just thought flash would work as a starting point.
1) I want to make a game that is abstract, involves movement, and digital art that looks like light. it responds to player input, and depends on it. i just want the experience to be about the interaction. This sounded like an doable beginner idea…maybe not. I want the light to look graphically appealing and try to understand how the animation and art works, with sound too. I don't really understand how the code-graphic-sound, would work together. but i think it's doable if i start small. then work up.
2) My other game idea is a hypothetical dragon that controls fire. also abstract, visually. the concept is about rage and arriving to peace. it's meant to look at aggression. I don’t really understand how it would happen though.
3) my other game idea is slightly story driven, but interactive. The story involves the growth of a young man, and a woman who seems to appear at the right place and time. It ends with her appearing to the player. It’s sort of a play on life. it’s too big to do, so i would just make a tiny piece of it. or just a concept. i thought of a way to design game play to involve the events. Yup.
These are vague ideas. Nothing I could really comment on.
Flesh them out more. Start thinking like a Designer. You want to make a game about light.
No. You want to make a Puzzle game involving X, Y and Z. The visual Theme should be "Light", what you mean by that is the objects the player is interacting with to solve the puzzles are different light sources.
And so on. If you want to go the professional route, a good GDD can measure hundreds of pages that describe how the game should look, sound, play, FEEL in minute detail.
So that it could be handed off to a complete stranger, and he does not need to ask "But character X, should she wear a bikini or full plate armour?"
You obviously don't need to do all that for a small game you create yourself. But try to flesh it out more. The sentences above are not even good elevator pitches. After reading them, I have no idea what you want to create. Other than idea 1 has to do with light (as long as it has a visual element, everything has to do with "light"), Idea 2 has a dragon that is angry (doesn't sound like a game yet), and Idea 3 is story driven (like 80% of singleplayer games), interactive (wouldn't be a game else), and that it is to big to do.
None of these "elevator pitches" would stir a lot of confidence in me that you know what you want to build there. Give us more details, and ask a question (should we tell you if they are feasible? What you need to do to build them? How much effort they are to build?)