Well the plot of land is technically given to him as an independent nation for him to keep and do whatever he want, then later Tsubaki's clan went employment looking originally to be employed as a future King but became already king of his small land because ninja's are skilled they basically became very sufficient capital citizens then later more immigrants, Kaosaka became his Prime minister that manages his Kingdom along with others ministers, with Touya learning along with the growth of his one village later town country. In a sense Touya is like a landlord who can live-off tax money(which he doesn't need or take) of the citizens that immigrated in his property but still actively participates in the management of his small Dukedom with the help of the ministers that came along the immigrants.

The situation of Touya is quite complicated but I saw where he resides in the map the land is very tiny how can he do anything.

In my personal opinion. I would say his absurd amount of "luck"(plot armour) should be held accountable for most of his circumstances. And I think he is responsible enough to manage his duchy, unlike "that guy"(can't remember if the word "brat" or lord was used to describe "him") from Eashen(Oda) that one of the Elite Four guys spoke of, before settling in Touya's country(Brunhild), for causing financial strife by raising the citizen's taxes, just so he can fill his own coffers. Unlike Touya, that lord was spoiled as whisical. And the citizens taxes; is nothing, but "chump change" to the self-sufficient Touya(his "cheat-like" abilities is also a contributor. Sorry Touya). As he barely even needs it, more than anyone.