Which language I should learn if I want to be a game developer? And is algorithm needed to develop a game?

Answer 1

I'd say JavaScript and Java would be your best bet.
JavaScript is very useful for making games on the web and Java for awesome offline/online apps. For example, Minecraft was programmed in Java and most of the apps in Android are programmed in Java. Hope that helps, good luck!

Answer 2

In this day and age, language is irrelevant. If you want to work for a game company, choose something mainstream. Google can tell you what those are faster than I can type them on my phone. If you want to work for yourself, it's more about vision and ingenuity than the language. That being said, the *tools* available for a particular language may impact what you can (reasonably) accomplish with it.

As for algorithms. Yes. You need them. Maybe not a bunch, but at least learn sorting/searching, hashing, and iteration (traversal). Even if you don't write your own containers or pathfinding APIs for instance, you should in know how they work well enough to optimize their use.