A good resource for your Dunkelweizen is in the BJCP Guide
. Your final gravity readings should fall in the 1.010-1.014 range, though that is dependent on whether or not the kit was designed along the BJCP guidelines. When using a hydrometer you should use a testing tube (like a big graduated flask) with enough of a sample of your beer to let it float. You generally want to avoid putting it directly in your fermenter, but if you sterilize it really well it will work in a pinch. You will also need to compensate for the temperature of the sample and a good calculator for doing so can be found here
It's not unusual to not see any violent airlock activity, especially with lower gravity brews. The foam and ring you saw are indicative of the krausen stage being over which is the peak of activity for fermentation. You can either leave it in your primary fermenter for 2 weeks or so or transfer it to a secondary a week after you pitched and leave it in the secondary for one to two weeks. Either way, you want to be sure your gravity readings are in that final gravity range and/or have held steady for 3 days before you bottle. If fermentation is still going on you run the risk of having "bottle bombs" which is a dangerous and messy mistake. Let the bottles sit in a dark, temperature controlled room (somewhere in the 70F area) for at least 2 weeks but preferably at least 3-4 to let them carbonate and age enough. Generally the longer they sit the better they'll be.
If you haven't already looked at it, I would suggest reading Palmer's online brewing book How to Brew
. It will answer many of the questions you have and give you a good foundation for your next brew.
Welcome to the hobby and good luck!