I've watched the anime and I think the story is epic although you have to get used of the 3d thing. Now here's my question: Does anyone knows until what chapter/volume of the manga did the anime covered? Your info is very much appreciated!

I don't know the answer to that question, but I can tell you that a second season is rumoured so we should get the rest of the animated story.

The anime continues to the summer.

I would recommend you to read the manga from the start. The reason is quite simple. The anime cut some of the arcs away and added something in the anime to make up for it. In my opinion it's not worth jumping those arcs over if you ask me.

Let me give you an example:

You get some omake chapters with the young kings concubine. She plays a role in showing how the people sees the king, how he really is, and what happens to her cuz she's the kings concubine. She got another concubine as best friend.

You also get to see assassin coming after the king and you find out about the scarf perso who's been together with Shin after they met eachother in the first battle. You know the person who's Shin's right arm but still much better at fighting that Shin.

So I would recommend you to read the manga to get the parts you wouldn't get if you only watched the anime or continued from the point after the anime ends.

Season 1 of Kingdom anime covers Vol. 1-16 of manga.

Season 1 covers 1-16 however in Season 2 they included the story of the woman who rescue the king in Zhao so I think they skip about one volume.

but they did actually use/shown this in the second season

They did not show Kyoukai, though it may be added later on in season 2, but at this point it has not appeared. They did however add the kings background history which they had previously skipped.