Q1.

What is the difference between the two methods to create static routes?

* The ip route 10.1.1.1 255.255.255.0 eth 0/0 command generates an ARP broadcast that looks for the next-hop IP address.
* The ip route 10.1.1.1 255.255.255.0 172.16.1.1 command does not generate an ARP request. It keeps Layer 2 out of the routing process.

What is the difference between the ip default-gateway, ip default-network, and ip route 0.0.0.0/0 commands?

The ip default-gateway command is used when IP routing is disabled on the router. However, ip default-network and ip route 0.0.0.0/0 are effective when IP routing is enabled on the router and they are used to route any packets which do not have an exact route match in the routing table.

What is synchronization, and how does it influence BGP routes installed in the IP routing table?

If your AS passes traffic from another AS to a third AS, BGP should not advertise a route before all routers in your AS learn about the route via IGP. BGP waits until IGP propagates the route within the AS and then advertises it to external peers. A BGP router with synchronization enabled does not install iBGP learned routes into its routing table if it is not able to validate those routes in its IGP