You should check out FF Brave Exvius on mobile. It's free to play and has all 3 of those.

It's turn based, and you get to use new and classic characters of the series.

You raise your level by fighting, though you can also use the equivalent of "gems" in other games to speed up the process.

It also has a world map, though it's more in line with the FFX world map where you can point and click to go back to places you've previously been, so you may not count that.

I think people are surprised at the depth this game has for being a ftp mobile title. You get to explore cities and dungeons, do side quests, and visit places you only unlock if you search to find them.