I am looking forward to develop game in java and might sell it as well so here is the question:

Do we need to pay fee to Oracle if we sell our game on the market or host it on our own web site with advertisement on the game page? Also can we sell software written in Java?

Do we need to pay fee to Oracle if we sell our game on the market or host it on our own web site with advertisement on the game page?

No.

Also can we sell software written in Java?

Yes.

You can market and sell programs that you write in Java without paying any fees to Oracle.

unless you decide to use commercially distributed third party libraries, you do not need to pay for the use of the language, nor to distribute any code or application you've written.

some authors of freely distributed libraries do ask you to include their name into your readme docs, and to keep their code as-is, but if you choose to use it, you usually do want the code like that, so ... meh, no problem there :)