f I have Xbox live Gold and I buy a game which has its price reduced due to Xbox Live Gold,...

If you bought the game, then it's yours and you can play it whenever you want, whether you have gold or not.

I have a one year xbox live gold and I see all this free stuff with gold and I try to buy it and it brings up the price of the game when I play multiplayer and and all taht that u need Xbox live which I need xbox live gold that my mom bought me for a year
I need instant help

yes you can,might be cheaper to buy a Xbox Live Family Gold Pack,which is 4 Gold Accounts for around the price of 2,its available via dashboard

Xbox Live Gold is not required to download games. You do however need gold to be able to play multiplayer in games that support it. They are some benefits to having gold, like getting 4 free games a month (2 Xbox One & 2 Xbox 360 via backward compatibility),
and also deals with gold, which changes each week with games sold at a reduced price. more info on the benefits of gold can be found here

https://www.xbox.com/en-gb/live/gold?xr=shellnav

You have Xbox Live its showing you have a Gold Account on here just be careful when Xbox is due for renewal as Microsoft will automatically renew it

I use CD Keys for Xbox Live usually get a good price on there website