No there aren't free versions.
There are three versions - Computer, console, and "pocket edition" (for ipads/phones/tablets).
Computer one costs £20, you buy online, it's a download. This is the original version and has the most features.
Following closely behind is the console version - for Playstation 3 or 4, and Xbox 360 or 1. This costs about £17, you can buy it as a download, or as a disc - look secondhand in Game, etc.
The Pocket Edition is a hugely cut-down version of the game for iPad etc. It costs £5. You buy it in the app store.
It's rated age 7 but there are two modes - creative, and survival. You can get monsters in Survival mode, but under-7s generally turn them off (this is an option). You can claim it's educational because it teaches them a bit of basic geology and some extremely basic concepts of chemistry (e.g. if you heat sand, you can make glass) and it has some components to build simple circuits. But mostly it's just fun, creative and harmless.
A youtube person called StampyLongNose makes lots of videos about Minecraft and children adore him. Parents love the fact that he doesn't swear but hate his laugh.
That's basically all you need to know!