Clans all have a rank and it increases as they win battles and rank up, this increases thier max party size. Vassals you create from wanderers start at rank 2 and normal clans are likely higher. It takes them time to fill up their party if they've been defeated or just made and they won't over spend, so if they have little income they may only have 1 party out and about. They also prioritize having some garrison too, so donating there if it's very low can help. But don't over do it or they will just throw out the troops if it costs too much.
More ranged units. You have to defeat their armies one way or another.
I don't know but I would use that castle to make new clan once you have 500 influence and spare wanderer. Fiefs and passive income is overrated, but more parties is always good!