If you are running Windows, it's pretty even. IExplorer has the edge in style sheets and integration with Windows programs. Netscape has numerous plugins and a better Java/JavaScript interface. If you are on the MacIntosh, I would say the edge goes to Netscape, although IExplorer is the only browser on OS X. If you are on linux, Netscape is your only choice.
No. There are several others.
There is no "best" way, but one of the most efficient ways is to look at pages you like, the use the View->Source (no the menu bar or on the right-mouse-click) to examing the HTML code. Cut and paste is a time-honored way of constructing web pages. Another way is to use a good search engine and ask the question "How do I XXXXX with YYYY" and sift through the results. Finally, you can go out and buy a book (or take a class).
Again, there is no "best", I have used Yahoo, Altavista, Excite and Google. Apart from the size of the database, the critical factor is in how you phrase the queries!
It is best to get into the habit because the next generation of browsers and parsers will be much more stringent. XML is very fussy about overlapping and unmatched tags.
Dynamic HTML is html which includes additional capability of being dynamically generated in response to user input. This is usually done in response to various "events" (such as onClick, onMouseOver, onMouseEnter, etc.) Netscape and IExplorer handle this in very different ways. The IExplorer browser has the ability to redraw itself without reloading the page (just resize the IExplorer window when there is content inside). Netscape must first reload the contents before redrawing. This limits what you can do in Netscape. The most robust methods for cross-platform dhtml rely on the use of <div> elements and the attributes of positioning and visibility.