RSVP tear messages are used to clear the PATH or RESERVATION states on a router instantaneously, which enables the reuse of resources on the router for other requests. This is essential in MPLS Traffic Engineering where efficient resource management is crucial for maintaining network performance and stability.

In this scenario, when edge routers at different regional sites are connected over a global carrier backbone, MP-eBGP must be run between routers to exchange customer VPNv4 routes. This is essential for enabling communication between customer sites located in different regions while utilizing a global carrier backbone service. Reference: Implementing and Operating Cisco Service Provider Network Core Technologies source documents or study guide

IS-IS uses NET addresses to identify each router in the network, and the NET address of each router must be unique. In order for IS-IS to establish connectivity between R1 and R3, the NET address of R3 must be different from the NET address of R1, but it must also follow the same structure. In this case, the NET address of R1 is 49.0133.532b.ca14.6915.21311.F40F.1B3a.ba10.00, so the NET address of R3 must be 49.0133.532b.ca14.6915.21311.F40F.1B4a.bb87.00.

The issue of no LDP neighbor existing for 1.1.1.1 between two directly connected routers could be due to R2 not receiving any hellos from R1. In the context of LDP (Label Distribution Protocol), hellos are used for the discovery of LDP peers. They are sent periodically on each interface that LDP is enabled on to discover and maintain LDP sessions with neighbors. If R2 is not seeing any hellos from R1, it means there's a failure in the initial step of establishing an LDP session, hence no neighbor relationship is formed.