Yes you can but if you are gaming at a low resolution an i5 with a slightly weaker graphics card would be better.
So try if the i5-3350p fits in your budget.
Not really. An I3 won't particularly bottleneck a HD 6950.http://www.tomshardware.co.uk/fx-4100-core-i3-2100-gaming-benchmark,review-32384.html
And you could play most modern games at sorta high/ultra settings in 1080p with that setup.