1) This is kinda up to you. I've gone back and forth with objectives but haven't found any compelling evidence that people really care about them. I've gotten plenty of callbacks without them. I'd Google some to see examples and tailor it to the position you're applying for.
2) Definitely add education if its mentioned at all on the posting.
3) You can't go wrong with an achievements section, especially if you have some. They are also great for boosting a resume with less experience.
4) I think this is worthless. Has nothing to do with the job.
5) I usually put that references are available upon request.
6) I would include a cover letter for each position your applying for a tailor it to the company, position and choose a handful of traits/responsibilities they want that you can offer. I created a generic cover letter to have on file with blanks for company name and position and I have a separate sheet with dozens of bullet points of what I have to offer (which are from previous cover letters) and use that to tailor each one. Then I save then for future reference or in case I get a callback, I have a record or what I offered. I think the cover letter is a great piece to include. I've gotten callbacks the very next day and my cover letters have helped.
You're welcome!