Career-change letters must say the bridge in plain language, then prove it with facts already on the resume.
Open with the target role and why your background is relevant in one sentence. Then two evidence paragraphs tied to the posting. Close without apologizing for the change.
If a claim is not on the CV, delete it from the letter. Interviews start from the documents.
Only briefly if it helps. Spend the space on proof for the new role.
No. Fix the resume first. The letter only selects from what is already there.