Sounds like a few problems.
Trouble shifting down to smaller chainring could be that the derailleur cable has stretched out, which is expected and normal. They can probably make a quick adjustment to trim this up. Another thing to consider is what gear you are at in the rear. Try to keep the chain parallel to the bike as possible to avoid "cross chaining". Shifting down can also be difficult if you are pushing really hard and the chain is under a high load.
Lastly, the chain coming off completely shouldn't happen under normal circumstances. Your limit screws probably need to be adjusted.
All that said, the bike is new enough that the Trek store should make all of these adjustments for free. Show some interest and they'll probably show you what they are doing so that you can learn about your bike!