last *n* posts, category, sidelines

I would like to know if there’s any way (template tags, hacks, plugins) to *play* with the WP tags (php) to produce some useful contents like the following – but important to notice that they should be (always) active while the main content of the weblog is displayed, say, in the central area of a weblog (they’re MT-like features I used to use on my old sites):
1) display the *last=n* posts in any page (say in a sideline of all pages), using just titles and/or just excerpts, and also edited by category (it can be an archive feature content, if it works);
2) display a similar sideline with *last=n” posts but fixed by any give month of the year;
3) organize a page with the posts by category, but in the order you want the categories to appear;
4) be able to use the *adhesive* plugin in any of the above “tricks”;
5) Is there any way to do all of those without the *if* php function?;
6) how to leave some content (say, a header, for example) out of the loop when using the *if* function to solve the problems presented here;
7) show different static content sidelines (i.e. not the main page posts) based on the content generated in the WP for different categories page?
Sorry for so many questions, but they’re all very similar to each other. I’ve tried to find answers in threads like this but no results.
Thanks.