Flak and mortar each have their ups and downs. Flak is a lot more reliable. It's easier to hit, and it'll get you more damage per shot. The mortar, on the other hand, has a high fire rate and much larger clip. As a result, its DPS is higher. At the same time, though, hitting at range isn't very easy at all. Especially on the Pyra, where aiming high to compensate for the drop can result in hitting the nosecone.
I'd personally recommend flak, but if your gunner/gungineer is good enough with a mortar then that's a completely viable option.
As for hwachas, you have to remember that there's that extremely long reload time during which the other ship is vulnerable. Since you have a gat on the front, you should ask your gunner/gungineer to target their hwachas and take them out. It's not that hard to do with a gatling if you're a decent shot and have heavy clip. You should also try manoeuvring out of the way. Hwacha projectiles travel fairly slowly, so a well-timed chute vent / hydrogen can be key in escaping damage.
What's also important is how your crew is responding to hwacha fire. While your front gunners/gungineers should obviously be getting their guns up as quickly as possible, the main engineer's job in keeping the engines going is more complicated. If they simply just rebuild the engines, they're going to get destroyed by the next volley. Have your main engineer rebuild the engines almost entirely, so that one more hit will bring them back up. After the next barrage, they can quickly get all three engines going long before the hwachas come in, giving you room to reposition.