Hey, anytime, I'm no expert at Wordpress, but I think I do have some decent performance optimization experience from other applications.
No, no, just commenting that I had to scroll down 10 pages to get to the bottom of your front page. That's a pretty big front page. This will probably be solved by your reducing the number of posts on the front page to 4, as you said!
No, it's a separate operation. Optimize tables is useful to run occasionally, though, as it cleans things up and also helps the query optimizer to best use the indexes once you've set them up. Oversimplifying, indexes are "lookup tables" used by MySQL to efficiently execute queries that would otherwise take a long time to run. They take up extra space and slow down updates and inserts (new posts, comments, etc), so you don't want to just add them willy-nilly. You do want to look at every query being executed against the database and make sure that the ones that hit big tables are using an index in order to avoid a full table scan.
Read this post from the Wordpress forum for some insight into the problem. The last few posts really do explain why unoptimized plugins are the bane of good Wordpress performance.
Basically, you'll want to do some analysis against your Wordpress database - a great opportunity to learn a very high-paying skillset!
The italics aren't enough?
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