Does repeating a dhikr multiple times during prayer, or repeating certain verses of Al-Fatiha, or repeating any dhikr, affect the validity of the prayer or invalidate its continuity? And does folding up one's trousers, which leads to the knees being slightly raised off the ground, affect the validity of the prayer?

The cure for obsessions (waswas) is to ignore them and not pay attention to them. Prayer is not invalidated by repeating a verse from Al-Fatihah or other remembrances like the tashahhud (definition), as stated by An-Nawawi and others. This does not break the continuity of the recitation.

Similarly, prayer is not invalidated by a part of the knee lifting from the ground as long as a portion of it remains in contact. It is sufficient to prostrate on some of the organs of prostration. For those who only require prostration on the forehead, the matter is even easier.