I don't think BGP has a problem working over IPIP
tunnels. In the end it is just a TCP connection to one or mre endpoints.
In principle yes, but unfortunately the current IPIP tunnel implementation
handles both the tunnel establishment and the routing. The routing is
static. You cannot setup BGP sessions because you do not know the other
side's address and AS.
Possibly one could work around that by adding the 44net endpoint address
and the BGP AS number of each tunnel gateway, so the endpoints could
connect eachother for the BGP routing.
However that would be another major change and I'm not sure everyone
would want to BGP peer with everyone else. That could also introduce
new scaling problems.
Rob