If I add wordpress to my site do I have to use there templates for my site because I really don't want to I would like to keep my layout that I hand coded myself. And is it possible to just install a plugin from wordpress to my site without installing wordpress?
One last question is there a PHP and MySQL plugin that will create a database and index all my web pages from my site in order to create an RSS feed.
You don't have to use wordpress templates! You can use the design you created, with a few modifications with wordpress.
It is not possible to install a plugin from wordpress w/o wordpress...that's why they're called wordpress plugins...
I think wordpress sets up RSS automatically, you just have to fish around in the preferences...
Try this and this for theme development reference.
See this site for RSS plugin info. For more information, try using google to find out how to convert your design to a wordpress theme.
I suspect there's two separate questions being asked in this thread which may not be related to each other.
Anyway, for the first question: You could reuse your existing template for your old website and adapt it into your custom Wordpress theme. Though I would say that theme development from scratch could be quite involved. If you don't like the learning curve of doing a Wordpress theme, you could opt to use an existing Wordpress theme and create a custom CSS to make it look like your existing webpage. I personally recommend that you could get a plain vanilla Wordpress theme like Sandbox and work the CSS from there.
As for the second question, if you are asking in the context of migrating your existing site to Wordpress: Wordpress automatically will generate the RSS feeds so long you port your pages into their "Posts" and "Pages" mechanism.
Do let us know and provide more information on what you want to achieve if you are asking the last question on a different context as in you have a set of webpages which you are not migrating to Wordpress but needing a means of needing an automatic means to translate those existing pages into a dynamic RSS feed.