With the R7 240 technically it'll work, but..
Civilization V is more dependent on a good processor than graphics card so it may be possible, but you might get slowdown or it might just take a long time when the computer AI calculates their actions on their turns. Your processor just slightly exceeds the
minimum requirements for Civilization 5, just so you know. Your PC technically doesn't meet
CSGO's minimum processor requirements (AMD triple core is recommended, you have an AMD dual core), but there are people who have played the game with processors similar to yours
(here's gameplay video from a PC with the 5000+ model, you have the 4400+ model). Given how close your PC is to the minimum acceptable specs, I'd aim for lowest settings possible, and I can't guarantee it'll be completely smooth, but it should be playable.
As for Youtube videos, I'm not sure a graphics card will help, as the main factor here is the outdated processor. It is possible for a graphics card to help in accelerating HTML5 Youtube playback, but I'm not sure if that's something that is built in and is already active on the latest Firefox/Chrome browsers or if it's something you may need to jump through some hoops to get working on Windows XP.