IOS – Apple captive portal detection does not pop up web sheet browser

I'm assuming you aren't using Lion, since your description sounds more like FileVault 1 (through Snow Leopard) than FileVault 2 (Lion).

FileVault 1 protects the entire home folder, with encryption when you aren't logged in and permissions when you are. In order to get to files in your Sites folder, the web server process would have to go through your home folder -- since it can't get into your home folder, it also can't get at anything inside it, so the permissions on your Sites folder are irrelevant. (I'd recommend setting the perms on Sites back to 755, though -- 777 is just a bad idea.)

As a result of this, ~/Sites is pretty much useless in FileVault accounts. Same with ~/Public -- normally, it's for sharing files both locally and (if the services are enabled) over AFP and/or SMB, but with FV it's not reachable.

But you do have an alternative: the top level web directory, /Library/WebServer/Documents. Just replace the default files with your own and you should be good to go.

iOS apps can only read data in their own directory and thus only Safari would be able to use these files - so how could you create them and put them in Safari's directories?

From Apple's Filesystem basics development documentation

An iOS app’s interactions with the file system are limited mostly to the directories inside the app’s sandbox. During installation of a new app, the installer code creates a home directory for the app, places the app in that directory, and creates several other key directories. These directories constitute the app’s primary view of the file system. Figure 1-1 shows a representation of the sandbox for an app.

Figure 1-1 Each iOS app operates within its own sandbox

Because it is in a sandbox, an app is generally prohibited from accessing or creating files in directories outside of its home directory. One exception to this rule occurs when an app uses public system interfaces to access things such as the user’s contacts or music. In those cases, the system frameworks handle any file-related operations needed to read from or modify the appropriate data store