Thank you. Here is the third part of my translation. I included synonyms in brackets. I really need you to check the words.

Integration into ongoing activities
1) Involvement of the classes of the participating students
2) Closer examination (or in-depth analysis) of propaedeutical knowledge
3) Mutual (reciprocal) knowledge of different cultures within European citizenship (exchanges through Internet and mobilities)
4) Transmission (transfer, transference) of both the experience and the results to parallel classes (I believe, for example students from other second classes whose students are not involved in the project)
5) Strengthening (boost, expansion, development) of the school’s didactic (or educational, educative?) and multimedia equipment.
6) Development of the capacity of using of ICT (information and communication technology)and of mastering English as a medium of communication (I don't know how to say that the study of English will be strenthen too)

Here are my suggestions for the third part of your translation:

Integration into ongoing activities:
1) Involvement of the participating students' classes:
- This means that the project should involve not only individual students, but also their entire classes or groups.
2) Closer examination or in-depth analysis of propaedeutical knowledge:
- This refers to a more thorough and detailed investigation or study of the foundational knowledge or pre-requisite knowledge required for the project.
3) Mutual knowledge of different cultures within European citizenship through exchanges via the Internet and mobilities:
- This means that students should have opportunities to learn about and understand different cultures within European citizenship through activities like online exchanges and physical mobilities or exchanges.
4) Transmission or sharing of both the experience and the results with parallel classes:
- This suggests that the project's experiences and outcomes should be communicated and shared with other classes that are similar or parallel to the participating classes.
5) Strengthening of the school's didactic, educational, and multimedia equipment:
- This implies enhancing or improving the school's teaching methods, educational tools, and multimedia resources.
6) Development of the capacity to use ICT (information and communication technology) and mastery of English as a medium of communication:
- This means that the project aims to enhance students' abilities to use technology for communication purposes, as well as to improve their proficiency in using English as a means of communication.