You shouldn't have any problems with configuring gre tunnels and cef. Cef is basically just layer-3 switching and a gre tunnel is just an interface. You should configure your tunnel as normal, there should be no problems with gre and cef.
EIGRP will use the same administrative distance and metric calculation for the GRE tunnel. The cost calculation is based on bandwidth and delay. The bandwidth and delay of the GRE tunnel will be taken from the tunnel interface configured on the router.