I'm not sure I understand you correctly. Are you planning on re-writing the text/content of a page that currently ranks #1?
If so, it *might* affect your ranking (I don't mean PAGE rank here, just the rank, as in, position in the results after searching). It very much depends on what you're changing. If you're not in a hurry, you could think about changing a single paragraph and then await the ranking results first before doing the next change.
Keeping your H[1-4], title and description the same will probably lower the impact a bit.
Meta keywords (as in, the meta keyword html tag) will not affect your ranking at all: they are not even crawled or indexed by Google.
Since you haven't made any change to title of the page and meta tags with h1,h2 tags the page may not be drop from the Google search for the major short keywords. Depending on the content updated you may have slight updation in the position of the long tail keywords.
Changing huge amount of content at once can drop your page for a short period. Search engines will have to reindex it and it will possibly make the "Google dance"... Keep you changes small and relevant to your pages contents.
This is simple. To avoid ranking drop while changing your content, you need to identify the repetition of the keyword on the page of your site that is ranking number 1. For instance, your homepage ranks number 1 in "web hosting" keyword. Count how many times this keyword has been repeated on the homepage in the code level (view source code and count keyword repetition). Let's say, 10 times. Now you go create your new homepage content and optimize it so to replicate the same repetition for the keyword the homepage is ranking number 1, which is, in this example, 10 times. If Google has counted the on-page factors on your site, maintaining the spread or repetition of the most important keyword while bringing in some new words will keep things in the safe level.
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Seems that you are going to change name of the page, it certainly will affect your ranking and authority. If it is really needed please don't forget to redirect (301) old one to new one. By doing this you can have all your SEO value to new page in some times.