1. You don't want to strength train the same body part 2 days in a row, and you don't want to lift EVERY day (so you need to take a rest day once a week). If you wanted to lift every day, you could split your body parts...I know some people like to train the front of the body one day (biceps, quads, abs, etc) and the back of the body the next (hamstrings, calves, triceps, back). Here's a good article on this kind and other kinds of "splits" http://exercise.about.com/cs/weightl...gthroutine.htm
2. Lifting sessions can vary in length, depending how hard you want to work the muscles you're targeting. If you're doing a split as described above, you can fit more exercises for the parts you're working into the same amount of time. You can add more or remove some exercises to fit the time you have available.
2 (the second #2!). This is a matter of training philosophy. You tend to see more muscle gain (which helps with weight loss...more muscle = more calories burned at rest) with a lower number of reps at a heavier weight. Some trainers, though, believe in doing more reps and a lower weight. There are different techniques (pyramid sets, for example) that use some combination of these to get results. These are typically based off of your one-rep max (the most weight you can lift for one full rep), and start with higher rep/lower weight, then gradually increase the weight and lower the reps. The bottom line is that there are a TON of schools of thought on this, and no one "right" way.
3. In terms of what you're missing, you really might want to try to find some cardio that isn't hard on your joints, but gets your heartrate up. Cardio is great for weight loss, and can help break up your lifting sessions so that you still get exercise most days, but aren't overtaxing your muscles by lifting on the same muscle groups multiple days in a row. And no, you don't sound naive.
Have you seen the "Ladies Who lift" forum? It's a great spot to ask these sorts of questions!