You do realize that a summoning is a ninjutsu, right? It has seals, even if Kishi doesn't bother to draw them anymore. Gai using summoning shows that he can use ninjutsu, but chooses not to.
Seriously, it's not difficult logic here:
-Summoning is a ninjutsu
-Gai can use summoning no jutsu
-Gai can use ninjutsu.
Also, for elements:
-All Konoha Jounin are required to know at least 2 elements
-Gai is a Jounin
-Gai knows at least 2 elements.
Extremely simple logic, I'm not sure how you can't grasp it. Especially when the databook, which is written by Kishimoto, shows Gai having skills in both Ninjutsu and Genjutsu. Which, by the way, indicates that he CAN USE THEM.