1) Involvement of the classes of the participating students: This sentence is correct.
2) Closer examination (or in-depth analysis) of propaedeutical knowledge: Both "closer examination" and "in-depth analysis" are correct phrases. "Propaedeutical knowledge" refers to foundational or introductory knowledge.
3) Mutual (reciprocal) knowledge of different cultures within European citizenship (exchanges through Internet and mobilities): This sentence is correct. "Mutual" and "reciprocal" can be used interchangeably here to mean a two-way exchange of knowledge. "Exchanges through Internet and mobilities" refers to interactions and exchanges facilitated by the internet and physical mobility.
4) Transmission (transfer, transference) of both the experience and the results to parallel classes: The sentence is correct. "Transmission," "transfer," and "transference" are all acceptable words to convey the idea of sharing the experience and results with parallel or similar classes.
5) Strengthening (boost, expansion, development) of the school’s didactic (or educational, educative?) and multimedia equipment: The sentence is correct. "Strengthening," "boosting," "expansion," and "development" all convey the idea of improving the school's didactic (educational) and multimedia equipment.
6) Development of the capacity of using ICT (information and communication technology) and of mastering English as a medium of communication: This sentence is correct. However, if you want to indicate that the study of English will be strengthened as well, you can modify the sentence to say: "Development of the capacity of using ICT and further mastery of English as a medium of communication." This indicates that the study of English will be enhanced and advanced.