Not necessarily, but you may put it in your resume. 'upon request'

From Job A to Job B, there will be a gap. Gap in a lot of ways, skills gap, experiences gap etc. How do you win the resume? 1st, find the common thing between Job A & Job B. Then, from that main point, you will restructure it in a way, focus on the skills that you may have from previous role and can be optimised to the next job. Even if you may have lack in any skills required for next job, make sure it all can be justified concretely.

In the resume, then you can emphasised certain point, while you can minimised other area so that they can see it clearly. And of course, this may help you to portray yourself efficiently. Good luck.

Not necessarily got header or not, as long as basic items that need to be put on a formal letter are there. Address? Yes it is needed.