(1) For the cover letter, should it end by saying something,
In my experience (~10 years on hiring committees, starting my second year as hiring committee chair), almost nobody will read your cover letter. If you have something to say about your research, say it in your research statement. If you have something to say about your teaching, say it in your teaching statement. If you have something to say about your personal life, don't.
If the department doesn't acknowledge receipt (typically by email), it's reasonable to call or email the department to double-check. But "waiting for your call" is unreasonably optimistic. Each department you're applying to probably gets hundreds of applications for each faculty position.
(2) Should the cover letter contain qualifications and skills like highly-motivated, fast learner etc?
Absolutely not! "Motivated" and "fast learner" are neither skills nor qualifications; they're useless boilerplate. Of course you're motivated and a fast learner; otherwise, you wouldn't have a PhD and a publication record consistent with a tenure-track faculty position. Your actual skills and qualifications should be apparent from your CV, your research and teaching statements, and your recommendation letters.
(3) Some recommends to mention potential drs from the department that the applicant can work with. Is this a good idea? If Dr. A is working on topic T, and I want to work on topic T, then should I say that I would like to collaborate with Dr. A? If yes, what is a good way to say it?!
Don't just say it; make a convincing case. Just dropping a few names into your research statement will be written off immediately as meaningless boilerplate. If your research goals really do converge with Dr. A's research interests, that should be obvious from your larger research narrative, and it should be easy for you to draw specific, technical, and credible connections between your interests and Dr. A's. Do not fake it. We can tell.
(4) For the research statement, should I use "I" or "we" for joint papers, assuming that I was the first author?
"We" or "my coauthors and I"; using "I" for joint work is dishonest. But this is a relatively minor issue.