Does the DOCTYPE matter when writing meta tags?
Only in so far as it decides if you need a /
at the end, and if the tag and attribute names are case sensitive.
Is meta case sensitive or not?
The tag and attribute names are in XHTML. The rest, depends on the specific meta data you are expressing.
Should I use comma between keywords or space? What if a keyword of your choice consists of two words, like "new ad"?
Meta keywords are comma separated (and all but worthless unless you run your own parser over them, search engines ignore them as they are rife with spam).
What else is important to think about in terms of SEO and meta tags?
Only description really matters, and the key is to provide useful information to display as a summary of the page (and to not use it if text extracted from the page is better for users).