MySQL:
I suspect it's an oversight that they didn't list databases in the Basic description. They say that it's perfect for blogs, and all blogs require a database (usually MySQL). They mention hundreds of PHP scripts, and almost every one requires a database (again, usually MySQL). I will post something in the Feedback section pointing this out.

Unlimited:
Uh, that's basically marketing fluff. Everyone does it, for fear of losing potential customers. While LP doesn't place a hard and fast limit on, say, bandwidth, they do limit CPU usage (on shared servers). Eventually, if your activity grows enough, and you use more bandwidth, storage, database, etc., you will bump into the CPU limit. And before you ask, no, there is no way to measure your usage and see if you're getting close to the unpublished limit. The first inkling of trouble is usually being suddenly suspended for excessive resource usage. Since LP can measure CPU usage, I don't know why they don't make this information available to us in some sort of gauge or report, or at least, send a warning when your usage trend appears to be heading towards the danger area. That would win them so many loyal customers!

Well, that's just the thing -- there are no hard and fast limits for anything but CPU usage (and email traffic), and that's a secret number (believed to be around 1% of the CPU). The only restriction on storage is that it must apply to your website -- no backing up your PCs onto your website. I suppose it's theoretically possible to, say, store a copy of every New York Times since it began publishing, for purposes of an archive site, and blow out LP's disks with 100 TB of data. In that case they'd probably just buy you off by refunding your account and telling you to get lost. The more stuff you store and people access, the more the CPU gets used and the closer you get to the tipping point.

I wish they would let us know what kind of CPU usage we're doing, so no one should be surprised (unless they were hacked) if they use too much.