IP tunnels are mostly point-to-point, so they aren't able to send or receive the broadcast traffic (more complex technologies exist, but lets leave them out of the scope for now).
So no, your setup is incorrect: you need to configure the remote address for a tunnel too. Yeah, the mask can be any that you can imagine, but effectively it will still be /32 - all other masks will merely confuse your routing stack, and most of the time things will work only if the mask doesn't interfere with de-facto /32 on this interface. For Cisco IOS it's common to have /30 or /31 masks, because of the legacy issues.
The latter means that you have to assign separate network prefix to an interface, or you won't be able to reach the networks behind the tunnel remote.
What about the 2.2.2.2 question - its form makes me think that you confuse inner and outer addresses of the tunnel. Outer ones are merely here to make sure the packet will be routed across the network where it would be dropped otherwise. For example, the packet with ip dst 192.168.0.1 isn't able to pass the WAN, - thats why in order to link the networks 192.168.0.0/24 and 192.168.1.0/24 via WAN the tunnel may be created, with outer IP addresses from public space. ip tunnel add usually contains outer (public) addresses, and ip addr add contains inner ones. This, of course, will be working if both pairs are private ones, but this setup is not intuitive.
