I plan on swing trading after six months of study and then six months of paper trading. I have a full time job and have to trade at night. I have considered penny stocks. Is it possible to trade them at night?
If you're looking for active trading at night, you'll need to either trade in a market that's open during those hours, or get into the futures market, which I don't believe covers penny stocks. I'm guessing that the penny stocks you're referencing fall into the realm of bio-techs and energy stocks (there are many more, but that's the trendy bracket). If you're in the US, those stocks are going to be on the NYSE and NASDAQ, which don't offer night trading other than some very limited after-hours trades and placing buy options that would fire off the next morning.
If you're going to be doing research for 6 months, I imagine you'll learn quickly that penny stocks are not worth your time/money and that you'll find more traditional stocks a better option, which means day-trading (in the sense of the term rather than time of day), is not a good way to go.
To my knowledge, penny stocks only trade during regular market hours, from 9:30 AM to 4:00 PM Eastern Standard Time, although you can usually take part in pre-market trading for an hour from 8:30 to 9:30, before the "official" open. Penny stocks don't really trade globally, and most don't have much volume anyway, so there's not much interest on the part of institutional investors.
All of this ignores, of course, the hazards of penny stocks, but that's another story.
Penny stocks can not be traded at night outside of the pre- and after hours. Another thing to keep in mind with penny stocks is that they frequently have big moves at the market open. This doesn't mean they're bad stocks, because of the shady name they have, there are also more opportunities. I would either daytrade them or keep them as long-term investments. Things to keep in mind are that most of these companies fail, and that they are susceptible to pump-and-dump schemes. If you're just looking for a safe investment strategy, this is not the place to be.