since you mentioned you are a beginner:

1. not a necessity. our body is capable of utilising proteins from various food sources to build muscle. https://www.medicalnewstoday.com/articles/196279

2. any generic calculator will do as it is not 100% accurate

3. leaner yes, but muscles you need resistance training. many jump rope tutorials in youtube often incorporate body weight workouts while jump roping

4. you learn posture fixing exercises instead. can check out some of athleanx videos

5. no need book. just try to see if you can go gym/workout for 3 times a week in a year then we talk.