Have xbox live gold for 6 months. Am I entitled to download the games offered free of charge or is this offer only for 12-month gold? And where in the xbox menu can you see which free games are currently being offered?
Of course you can download the games. Gold is gold no matter how long.
But keep in mind that the One titles can only be played with a valid gold subscription, whereas the 360 games remain available even after they have expired.
You can download and view them directly in the main menu. There's always an advertisement for the gold offers directly in the first row with tiles. Just click on it and the first thing you see are the free games.
Alternatively, you can see memberships in the store under the large tiles of one of the fields. Your gold membership is listed there. Also press it and you will see the games.