Hi VirgoChic! Congratulations on starting your exercise program!
Here's my thoughts on your two questions ...
First, the arms on the treadmill may add a little bit of extra cardio to your workout but aren't resistance training. If they had enough resistance to count, you'd only be able to move them 12 to 15 times before you had to rest. Instead, I think they're designed to be used throughout the whole cardio workout and so are lightweight and easy to move. But I'm sure they burn a few more calories when you use them and that's a good thing!
I would definitely add in resistance training - both upper and lower body - to your treadmill cardio for a complete exercise program. It will help burn off the fat, keep your metabolism high, and give you that tight, toned upper body that you're looking for. For some ideas on starting with weights, check out our Ladies Who Lift forum here - there's a 'sticky' with ideas for starting a weight routine.
You're right, rest days are primarily geared toward weightlifting in order to allow muscles to rest and grow. You don't HAVE to take a day off from cardio but most people take off at least one day per week. I ask my clients who want to lose weight to start off with three days of cardio per week and work up to five or six, which is plenty. It's really a matter of your schedule and personal preference.