What is lowest allowed entry age in Germany to participate in pc e-sports?
Depends on the game. For League of Legends the required age for playing in the LCS is 17. But this is a decision by them, not by the law. See EU LCS rulebook 1.1
By German law, basically when you are allowed to officially work, i.e. 15 years old. It may be possible to get exemptions for that if it only applies to a single event and doesn't interfere with school. Keep in mind though, that this all requires consent of the person's legal guardian (i.e. parents in most cases). See German youth work laws. "Das Mindestalter ist 15 Jahre..." - The minimum age is 15 years old. In the future, when LCS becomes an accepted sport in Germany junior clubs may emerge, where you may compete at a younger age (e.g. for football the youngest teams are F-juniors, who are 7-8 years old). But I think we are a decade away from that.
In any case, I'd highly recommend finishing at least Realschule/Mittlere Reife before diving into an esports career full time. I also recommend this answer on Quora which provides some first hand insights of the challenges a young person trying to launch an esports career might face.
Bit offtopic addendum, but I feel it may be important for aspiring players: I feel young people often have the misconception of going pro in a videogame is an easy career choice. What's not to love? You play your favorite game and earn money doing so. They often underestimate the amount of work and time they have to put into that game, keep in mind that going pro means you play that same game 50-60 hours (nearly) every week and that for 5-10 years. Esports is still very young and only a profitable career to the top 100 - top 1000 players of the game. Also an esports career is often very short, only very few players manage to stay on top until their late 20s, many players start their career at 15-16 and retire at 23-24. Having at least a decent school education to start your life after esports is paramount.
If I were 15 right now, enrolled in Realschule and wanted to try a career in esports, I'd take this approach: Focus on school as much as necessary to earn good grades, play my game of choice as much as possible to practice. After I finish 10th grade, I'd take a look at my chances. Am I very highly ranked? (e.g. for LoL at the very least Diamond 2, preferably Master or Challenger). If yes, I'd focus all my effort on the game and try to get a spot in a semi-pro or amateur team (getting the appropriate contacts beforehand would be very helpful). Now, the luck factor comes in: I'd have to perform in smaller competitions and get scouted by a more competitive team to get my first contract. From here on everybody has to decide for themselves whether they continue or switch to a different career and also how to make a living while not being under contract. In the bigger esports games you might be able to earn enough money while playing in a semi pro team.
It really depends on the game the competition is for and who organises it. The German government, as part of the formation talks, did agree to recognise E-sports as a sport, but it is not yet clear what that exactly entails for stuff like minimum age to compete etc.
However, Germany has strict age gating rules for many games. For example, you can't play PUBG under 18, Counter Strike under 16 or League of Legends under 12. Most organisers won't allow a player who is below the legal minimum age to compete or even to spectate in order to adhere to these laws (which has lead to situations where foreign teams with different local age laws couldn't bring one of their players because they were in between the 2 ages).