It's kind of hard to figure what you're trying to do.. What are you "brewing"?
Using a hydrometer, you would know it's finished when you take several reading and density is stable. Without a hydrometer I would check how much CO2 is produced. You mentioned an airlock, is it bubbling? Also, it might depend on the type of yeast and how much you used. White sugar is a "complex" sugar and it's hard to know how the yeast will work with it. If you were producing a beer, I would suggest two weeks of fermentation to be safe.
A lot of people will discourage you to use more than 1 vessel for fermentation. It has been tested that it doesn't provide anything and increase the risk of contamination. That being said, secondary fermentation refers to the phase where yeast has done much of their work. It's usually the phase where it refine and clean some by-products. People add things during second fermentation because there's less CO2 produced so more aroma is kept.
Plastic is fine as long as you use proper sanitation. Never used a plastic that is cheap. I would check if it's BPA free, etc.
If you're using proper sanitation, then you should be OK. Fermentation isn't distillation so there's no concept of producing "wrong" alcohol. Worst that could happen is contamination. You should be able to see, smell or taste it.