Do I need Lion on a MacBook to use iCloud?
1. Can I use iCloud to back up all the files on my MacBook?

iCloud is used to store the data that an iCloud enabled application has saved.  It is not a backup mechanism for your Mac, however in principle it can form part of a backup system.  iCloud doesn't show up as one simple folder on the mac that syncs (the DropBox model of cloud storage) but instead has a fairly well hidden folder in ~/Library for ad-hoc syncing/backup and instead requires each application to tell the mac which documents should be cached locally and "stored in the cloud".

For example, if your system is modern enough to support internet recovery, then you effectively have the OS not exactly backed up as such, but available for a restore withut the need for having copies of the physical media.  Of course, you lose your system preferences, user accounts and indeed everything else, but you can recover an OS installation to a default level easily.  On top of tis, if you then login to your Apple ID on the App Store, you can then download all your apps that you have purchased.  Of course again there is no guarantee that this will be all of your apps, but for some it may well be.  Once you have recovered your OS and your Apps, any Apps that use iCloud will then have their data available for use.

So, in certain scenarios it's the final pin in the recovery of your data, but it's by no means by itself a full backup solution, and you will need to cater (preferable via Time Machine) for a better solution unless you never change your prefs, and only use app store apps. Think of iCloud as storing just a few critical documents from just a few critical apps, and not currently a viable total backup solution.

2. To use iCloud, do I need Lion installed (as opposed to older Mac OS)?

Lion (OS X 10.7) is the minimum OS version required to use iCloud, You can gain access to the App Store from 10.6.6 onwards which is the only place where you can download iCloud enabled applications anyway, but be aware that just because you can buy an iCloud Enabled App Store app pre-Lion, you may not be able to use it.

3. After I've bought Lion, is there a fee to use iCloud with my mac?

There is no seperate iCloud fee, accounts are free in perpetuity, although obviously the apps that use it may have a cost associated with them. Additionally, the free account includes 5 GB of cloud storage, so you may run into fees should you need to store more data off site than the free allotment. Yearly storage costs begin at $20 (USD) to add another 10 GB (so 15 total storage).