There is a tunnel under Cyseal with a couple entrance in town, if you search, or dig (see spoiler above).
The easiest gate to leave by is the only one that is open, behind the King Crab.
For combat near the gates, guards will come out to help if the gate is open, and you can use Arhu's ballista.
Investigate the murder to advance the main plot. First get a list of suspects (examine the crime scene, look for the body) and then narrow them down (search for evidence, or if a character has Pet Pal, talk to Jake's dog Murphy).