I'm wondering if the spiders read layers like any other html page.
When you view the source code at the browser level, that is exactly what the spiders will see. Do you see any problems with your layers as they are currently set up?
I've also read that it is better to link style sheets externally. Is this normally true?
Normally yes. You'll have your global styles that apply to all pages and linking to those externally is the suggested method.
You may find that working with embedded styles on certain pages works too in addition to the externally linked global style sheet. Embedded meaning that the styles are within the <head></head> section of your document.
P.S. In regards to layers, you might want to be careful when using visibility. Make sure you are not hiding anything that should be visible. This can get a little tricky.