Mini Metro. Its a transportation strategy game where you build and manage a city´s metro system through the style of the London tube map. You pay once and get the whole game. No ads or micro transactions.

Open Tyrian is an old shoot em up thats open source and has been ported to dozens of platforms, including android. It plays very well with touch controls.

If you want a Minecraft like game thats free and has no microtransactions I recommend Minetest (Now called Luanti). Its open source and has tons of mods.