yes all will work fine.
you just won't be able to max skyrim since its cpu bound and only really works well on an OC'ed sandy bridge cpu.
you'd still play well on high.
Actually thats not really true.
" This game clearly relies on CPU power, and you need a Sandy Bridge-based Core i3 at 3 GHz or a Phenom II at 3.5 GHz to provide a minimum 30 FPS. Bear in mind that we're using the ultra detail setting here, and processing requirements drop significantly as you start stepping back. So, you can make due with a less potent chip when you dial in detail options appropriately. "http://www.tomshardware.com/reviews/skyrim-performance-benchmark,3074-9.html
It will run fine on Ultra on your system OP.