BGP is a routing protocol that operates between autonomous systems (AS). An AS is a group of routers under a single administrative control. BGP can be classified into two types: internal BGP (IBGP) and external BGP (EBGP). IBGP is the BGP communication between routers within the same AS, while EBGP is the BGP communication between routers in different AS. BGP uses the AS_PATH attribute to record the AS numbers that the route has passed through, and uses it to prevent routing loops and select the best path.

In this scenario, you want to add a second ISP connection and remove the default route to the existing ISP. This means that you want to have more control over the routing decisions and use BGP to exchange routes with both ISPs. To do this, you need to deploy the BGP protocol in your network and configure both IBGP and EBGP sessions. The correct statements about BGP in this scenario are:

IBGP peers advertise routes received from EBGP peers to other IBGP peers. This is the default behavior of IBGP, as it allows the routers within the same AS to learn the routes from different EBGP peers and select the best exit point. However, IBGP has a rule that it does not advertise routes received from IBGP peers to other IBGP peers, to avoid creating routing loops. Therefore, option B is correct and option C is incorrect. To overcome this rule, IBGP requires a full mesh topology, where every IBGP router is directly connected to every other IBGP router, or a route reflector or confederation design, where some IBGP routers act as intermediaries to reflect or aggregate the routes to other IBGP routers.

EBGP peers advertise routes received from IBGP peers to other EBGP peers. This is the default behavior of EBGP, as it allows the routers in different AS to exchange routes and reachability information. However, EBGP has a rule that it does not advertise routes received from EBGP peers to other EBGP peers, to avoid creating routing loops. Therefore, option D is correct and option A is incorrect. To overcome this rule, EBGP uses the AS_PATH attribute to filter out the routes that contain its own AS number, or uses route maps or policies to control the route advertisement. IBGP does not update the next-hop attribute to ensure reachability within an AS, as the next-hop attribute is preserved by IBGP. Instead, IBGP relies on an underlying IGP (Interior Gateway Protocol) to provide reachability to the next-hop.