Yonathan died young, during the war with the Pelishtim. Did he leave children?
Yes, he had a son Mephibosheth (Shmuel II 4:4).
Yes, in Divrei Hayamim I 9:40 it says
וּבֶן־יְהוֹנָתָ֖ן מְרִ֣יב בָּ֑עַל וּמְרִי־בַ֖עַל הוֹלִ֥יד אֶת־מִיכָֽה׃
And the son of Jonathan was Merib-baal; and Merib-baal begot Micah.
So he had a least one child named Merib-baal.