What is RRCConnectionResumeRequest-r13 in LTE?

It is the uplink LTE RRC message the UE sends to request continuation of a suspended LTE context.

What comes after RRCConnectionResumeRequest-r13?

The network may respond with RRCConnectionResume-r13, or the branch may fall back to fresh setup.

How is it different from RRCConnectionRequest?

RRCConnectionRequest starts a new connection. RRCConnectionResumeRequest-r13 tries to continue a stored suspended one.

What should I inspect first in RRCConnectionResumeRequest-r13?

Start with whether the branch is really a resume path, then inspect the resume identity fields and the next network response.