Trying to answer as best I can: Your culture won't smell like alcohol and it won't smell like bread yeast. It will have it's own unique sourdough smell.
Yeast gives off alcohol as part of the process. Different yeasts have different tolerances for how much alcohol they can stand. Basically once the alcohol gets to a certain concentration, the yeast will go dormant. Similar mechanics with beer.
The fact that your cultures doubled is good news. But remember, once the yeast exhausts the available sugars in the flour, they will stop bubbling. That's normal.
If you are leaving your cultures out at room temp, you'll exhaust those sugars quickly.
When I refresh my culture, I leave it out on the counter until it's bubbling and has almost overflowed the container. At that point it goes into the fridge. I will leave it there up to a month before doing another refresh.
Hard to explain but your culture should have a sourdough smell. I can't think of anything to compare it to. Using supermarket sourdough for this may be an exercise in futility as those breads can be pretty lame. My guess is there's nothing wrong with yours.
The only thing I can think that's different from what I do is leaving it out at room temp for more than half a day.
You can abuse sourdough starter up to a point but once you say you're sorry it's your friend again.
Time to make some bread?!
The instructions should read to throw away half the starter if you haven't used it to make bread (i.e. the starter needs to be refreshed in order to continue living). If it doesn't get new flour and water, it has nothing to keep it alive. So it tells you to get rid of half (by baking or, at worst, chucking it out). You could keep it, but you would end up with a hell of a lot of starter (exponentially!).
As for food safety, I don't think you have much to worry about... However I'm sure some of the other food scientists on this site will regurgitate a bunch of stats for you soon...
Best Answer
If it has mold on it then it needs to be thrown away, you are unlikely to salvage it. Once a sourdough starter goes wrong it's generally not worth your time to try and save it, just start over.