1: Besides speed (which PHP has lots of) php is a language that is easy to code in for most beginners, yet advanced enough to keep most pros interested and not make them feel "boxed in" like many canned packages like cold fusion. Also, almost any web server and OS combo you can think of can run PHP, preventing worries about scalability and vendor lock in.
PHP is very extendable, so much so you can write your own modules. Want a database connector for a database no one uses? You can hire a programmer to do it for you or roll your own. Since the source is available, there's plenty of examples to look through.
2: Yes, search engines can search your pages. Note that if a search engine is programmed to only view pages ending in .htm or .html, you can set up apache to serve .htm files with php inside.
3: PHP drawbacks: While PHP supports OO programming, it's not as mature as Java or Perl or C++. You really have to know how to run build files from tar balls to get the most out of it, but that's true with most open source software.
4: PHP is programmed right into your html page just Microsoft's ASP is. It's a little easier than Perl, a little tougher than Visual Basic and Cold Fusion.