An Erasmus motivation letter should cover academic fit, language readiness and your reasons for choosing that host country. Selection panels weigh adaptability heavily, so give evidence of it.
A cover letter targets a specific job and its requirements. A motivation letter targets a programme or opportunity and focuses on your reasons and goals rather than your qualifications alone.
One page — around 400 to 600 words. European admissions teams generally expect brevity, and exceeding a stated limit counts against you.
No. The CV lists what you did. The motivation letter explains why it matters and where it is leading.