Organizing in Lightroom

I’m just starting with Lightroom 4 and am a bit puzzled regarding organization.  

I'm posting my question here as proof of my engagement with photography technology, which my tutor may be reviewing in the not too distant future.  Since this blog has a tiny readership, I'll be adding links to this post to a few forums to elicit advice.  Please feel free to add a comment here, or in the forum topic that brought you here - or both.  

Here we go.
 

As I understand it, there are three branches of the LR file tree:

1. Catalog – the equivalent of the My Photos folder on my internal hard drive
2. Folders – the equivalent of all of the topic related folders in the My Photos folder (for example, photos from a recent visit to the ball park is 2012.08.13 Turner Field)
3. Collections – the equivalent of playlists, photos spread across any number of folders and grouped by tags

All of the data for these folders is stored in the Catalog file, regardless of where the actual photo files are stored. 

Am I doing ok so far?

Questions:

1. Does it matter where the Catalog file is stored?  Should it be stored to the same HD to which the actual photos are stored?  Can the Catalog file and the actual photos be stored separately:  the Catalog file to the internal HD, the photos to the external?  Is that a less than optimal set-up?
2.  How many Catalogs do you typically maintain?  At present I have one folder on my external HD called Photographs.  This contains hundreds of sub-folders by date-topic.   I can’t now see the need for multiple Catalogs.  Am I missing something?  This photographer says he creates a new Catalog each year.  This writer suggestions Catalogs based on Professional and Personal work, or themed Catalogs.  (He also notes that the LR search function will not work across Catalogs.  Is this true in LR4?)  Any other options or suggestions?

Thank you for reading this far, and for any help you can provide.