Many Players vs. Fewer Players
Depending on the amount of players, there's both advantages and disadvantages. You should be aware of both of them.
In auctions, with more players, more people are putting things up, so you should be able to find more cheaper items to bid on. However, there are also more people bidding, so you might have to bid higher to win.
With the trading post, there are more things up, and you can actually bid lower. That's because there are more younger players, that don't know the actual value of the items.
Personally, I like the trading post with a lot of players on. You don't see the same old things over and over. Also, with younger players, they will take less cause they are just putting their "Something has happened!" items up for trade. Most older players would put it in their shop.
Also with more players, neopets lags. You shouldn't be upset because it's lagging for everyone. Just bid a bit earlier to make sure your bid got in. I know you would like to bid at 1-2 seconds, but you bid probably won't make it in time, so bid earlier, cause everyone else has to as well.
If there are very, very few people on, you can refresh till about 3 seconds and still get a bid in. I don't do it because I don't want to risk it, but you can. It refreshes quickly and if you're fast enough, can still make a bid.
After neopets has been "down" for a while, play like there are very few players on, because there are fewer players. Some have decided to do something in their real life since neopets was down, or they just don't know neopets is back up. However, there are some compulsive types that will keep trying to get back into the site, for hours.
One time about when the site is acting up, bid on the auctions that are about to end. Bid on all of them, even there is a minute to go, you just might win, since people aren't able to get their bids in.
With quests, do them when there's more players, so in the day time. I don't do quests, but if that's your thing, do it in the day.