1. Do weights before cardio if you do them on the same day. This is better for the workout as well as helping with fat loss during the catrdio because the weight trainingf will use up glycogen, which will for the body to use more fat when you do your cardio. Otherwise, alternate days.
2. It is not easy for women to get bulky due to the lack of testosterone, so please don't avoid the heavier weights like walking near them will turn you into Chyna.

It won't happen. You'd really have to lift hard and often and eat the same way.
To start, use presses, rows, squats (using a smith machine or just leg presses) and crunches which will hit all the major muscle groups. Find a weight that you can do 3 sets of 10-12 reps with. The last reps should be hard, but not to the extent that your form crashes. Just remember that if it is too easy, it's useless. You have to stress the muscles to get anything out of it.
Hope that helps.