where on earth did you hear you gain fat with muscle?
With the exception of novice trainees, who can put on some muscle mass without a change in diet, in order to properly gain muscle you have to ingest a surplus of calories. Unless the trainee can dial up to the exact number of calories, they will not be gaining enough to fully maximize their growth. Thus some fat is gained by the excess. Close to every lifter will attest to that.
As long as you don't negatively change your diet with your workout routine you wont gain fat.
Depends on the previous diet, but yeah kinda.
As for muscles, if your wanting to bulk up or build strength then the high weight low rep routine is the way to go.
If your looking for a toned/cut and endurance training then a lot of cardio and low-med weight with high reps is good.
Kinda there, but progression and diet are the most important thing in gaining weight. You can go low reps or higher reps, but as long as you're lifting heavy, progressing through weight, and eating enough you'll grow.
As for losing weight, diet is most important again. If you're burning more calories than you ingest you're getting there. But don't forget to lift heavy as well to fully tax your muscles.