Well, I'm guessing you racked into secondary after a week or 10 days so more than likely the aggressive fermentation phase is complete and there will not be much activity in the secondary airlock, maybe none at all and that's ok.
What many beer kit instructions tell a person is to rack to a secondary after 7-10 days and then let sit. Some even say bottle after 7-10 days. That is generally a marketing thing. Most all homebrewers do that at first. Then, for the love of brewing join a form like this one here and find out the home brew stores don't always provide accurate info, some do and some are more interested in bringing new brewers into their market. The info they tell you or instruction they provide will make beer but if you want to make really good beer.
Time is your friend.
Secondary fermentation in a different carboy/bucket is not a must do.
Temperature of the fermenting wort (not ambient air temp) is very important
Time is on your side.. the longer the better.
Infections are uncommon, especially with the sanitation products readily available.
Ya know, I think I forgot your first question.. Not really. The only true way to understand what is happening in the fermenter is to take specific gravity readings with a hydrometer. You take a reading after the wort is cooled to yeast pitching temp and before the yeast is added. Note it, you should be well within the range the recipe calls for. This is the original gravity of your wort (soon to be beer) Next add the yeast. After about a week or two take another gravity reading and you'll see a significant drop. If the drop is near the recipes final gravity then it's probably ok to bottle, just take the reading a few days in a row to make sure it stays the same, if it keeps dropping the yeast are still doing there job eating sugars, farting co2 and peeing alcohol. Once the specific gravity remains the same a few days.. bottle it up.
Sorry for the long answer hope it helps a bit. Read up on these forums, especially go to the Beginner Brewers section, a ton of great post there that will answer many questions. Brewing is like anything else, it takes time to understand.
Okay.. last bit of unwanted advice. Time and patience are some of your best freind's when it comes to brewing beer.