1. You burn more calories if you do cardio before weights.
As you fatigue the second workout will be less intense and therefor burn less calories than the first workout. Do the main focus workout first. If you are marathon training then run first. If you are working on improving your 1 RM on squats then lift weights first.
2. The cardio equipment at the gym accurately records calories burned.
Cardio equipment at the gym is notoriously off (incorrect) when recording calories burned. A more accurate way to know your calories burned is to use a fitness band/watch or an online calories burned calculator.
3. Poor eating habits can be erased with tough workouts in the gym.
While in your teens and 20’s you can try to get by it will eventually catch up to you at some point. Excess sugar, calories, alcohol and poor nutrition habits will cause poor health. A good way to avoid these pitfalls is to record your daily food and drink intake in an app that will give you the nutritional breakdown of your habits. This is one of the easiest and quickest ways to lose weight.
4. Women who lift weights will get bulky.
Women do not have enough testosterone to build bulky muscles like men. Women need to incorporate resistance training to maintain muscles for strength for everyday activities, to increase metabolism and be toned (not squishy). In order for a women to maintain a large amount of muscle mass they have to perform a lot of resistance training, consume a lot of protein (and possibly supplements) and eat a lot of calories to support and maintain that mass. They go out of their way to purposely achieve those results.
5. You need to drink a protein shake after every workout.
A protein shake is a meal replacement. That means you drink it instead of a breakfast, lunch or dinner. Depending on the calorie content you could make it a snack. If you really want to down a shake post workout then incorporate it into your nutritional plan for the day. You could hit then gym then have a shake for breakfast. You could do a bodyweight routine at work and drink a shake for lunch. You could do an evening commute run home and then have a shake for dinner.
6. To get a ripped 6-pack you need to do a million crunches.
There is no way to spot reduce. Abs, biceps or calves development are all going to be dependent on several factors including your genetics, nutrition, workout program, etc. Instead of focusing on 1 particular body part try to focus on your overall total body. If you want to see an increase in muscle definition then focus on a workout program that will use cardio and resistance training components and reduce the amount of processed foods you eat. Try to switch them out for organic, whole food, fresh (or canned with low sodium) food options. In 1-3 months of making these adjustments you should notice your body feeling energetic, clothes fitting better, etc.