Alright, i tell you it's a official wordpress.com plugin offering combined services in a single package but none of them is able to speed up your wordpress site.
Yeah i have tried it many times but its very buggy wp-minify adds a little more into the mix i do think that w3tc will eventually develop the minify to an extent that it will fast become the best out there
It's basically a official wordpress plugin, that enables WP stats - a tracking service pretty like Google Analytics but this one is optimize specially for wordpress blogs, second thing it comes with Sharedaddy a worpress plugin built-in that allows you easily set up your own social sharing buttons within few clicks, third is after the deadline a plugin that lets you spell check your posts before publishing them, fourth is a twitter widget for your site, fifth is a URL shortening service by wordpress known as Wp.me, sixth is Gravatar hovercards, seventh is Shortcode embeds pretty neat way to embed code into your posts for videos & other stuff and last one is latex. So, Jetpack is combination of these eight services comes in a single package.You can get it from wordpress.org and i had also attached a screenshot
Yes, it's right but it also increase the number of your and could make our site slow. If you want to optimize your database you can do it via phpMyAdmin on your hosting. But if you want to optimize automated and scheduled, use a plugin could be the best way. You can try WP-DBManager. It has good option but it doesn't work on some hosting.
The only thing I can recommend is that you optimize your themes. That should save a little space on the site and make it run a lot smoother.
If its a large wordpress site with a lot of saved page/post revisions, try deleting those revisions with a plugin called better delete revision My site was loading VERY slowly, I tried a bunch of the cache/compression plugins and clocked the improvement, and it didnt make much of a difference. Once I deleted my revisions and cleared up the database, the site loaded quickly again.
If you want to notice a huge difference I would suggest you setting up https://www.varnish-cache.org . It's best you can do for your site.