Q: Do you think it's good for a level 3 to be able to do level 4, 5, 6, and 7 skills on all the events?

Sure, why not? Some girls focus only on the skills that apply to their level at any particular point in time, but other girls might begin to work skills for much higher levels long before they actually need to compete those skills. It all depends on your the way your coaches want to do things and their particular coaching styles.

Ex: When I was a level 5 (close as I can get to your scenario, as I didn't compete level 3 or 4), my coaches had me focusing only on level 5 skills and routines during my competitive season. But the second the last meet was over, we began our summer training, which meant that we stepped up the hours per week in the gym and started to focus not only on the next level's skills and routines, but also on higher-level drills to help prepare us for the future. The summer before my level 6 season I was working clear hips, back tucks, and all the other skills needed for level 6, but I was also working double backs into the pit, straddle backs, handsprings on beam, arabians, and other skills that would benefit me up through about level 9. Because we increased practice hours, we had more time to focus on more difficult skills. Not only was it good prep for future seasons, but it also helped with body control and conquering the fear issue and all that other stuff. However, when I moved out of state and switched gyms (during the summer before my level 7 season), I realized that not all coaches utilize summer workouts that way. At my new gym I focused solely on perfecting my routines and skills for the upcoming level 7 season, and that was absolutely fine as well.

I'm not sure exactly how your coaches train you, but the purpose of my example was to show you that each coach has his or her own system for preparing their gymnasts for the upcoming levels. Some coaches take it strictly one level at a time, others don't. Personally, I enjoyed being able to train higher-level skills during the summer. I found it useful in later years, and I also just found it to be something new, interesting, and exciting. It helped me to really stay engaged in the sport during times I might've otherwise felt burned out. But that might not work for everyone. I think it's perfectly acceptable for you to focus on the level at hand. It's okay if you're not ready for level 7 right now, and it's okay if you don't have all your skills even for the next level. Work at your own pace, that's the most important thing to remember. I know that it's incredibly frustrating to feel like your progress is slow, but that's something every gymnast goes through.

Wow, I'm really blabbing. The moral of the story is, yes, it is okay to be working level 5, 6, or 7 skills during level 3, as long as you still feel prepared for the level you're competing right now. It might even be beneficial, depending on the way your coaches handle it and the way you prefer to progress in the sport. But if you can't move that quickly and prefer to focus on the level you're competing NOW, that's fine too! Lots of gymnasts work that way. Be patient with yourself.