Well, you say you have old version, it is best to have latest versions on all devices you have game. This would also ensure that save files work (save files can be exchanged between all platforms), as there might be some problems if you use very different versions.
You need to buy only once per platform, but for each platform, as each platform is owned by different company, you need to buy again. Although EK is made by one man, it is sold by different companies (Android - Google, iOS - Apple, Steam - Valve) and each company wants their share, that's the reason for purchasing again.
About multiplayer, probably not, development is finished for the moment. Developer works on his new game.