And as I stated before, your budget really isn't high enough to grant a full system overhaul while maintaining performance figures that are actually decent and worth the money and effort. That's been my point all along. Try to remember as my article stated, the brute force in gaming is the GPU. At your budget the best option is to upgrade the GPU which is why I've been insisting on it.
Things to look for in GPU are performance figures in your budget. The model and amount of VRAM aren't too much of a concern. Don't be tricked into thinking a card is good because it has 4GB of RAM or anything like that. Little hint, anything under the *50 cards in the Nvidia side of things is just junk and not worth the time.
Maybe I don't understand, but I don't see how you buying pieces is relevant if he is anyways. What's the difference to him? An upgrade is an upgrade. If he wants to buy you a new computer then let him, just make sure to get something decent and capable of what you want to do with the computer.
With your budget, no your HDD is fine.
Buying better than what you need in your budget range is essentially what you want. For instance the PSU I listed can be used in many future builds as decent video card power demands are lowering every year.
I recommend anything Intel and dual core based on the 1155 socket. Cheapest solution.
Any case that is ATX and cheap. Just don't forget, a new case and computer means you need a new PSU. If you buy anymore than 3GB of RAM you will need an OS which will cost around 80€ which is about 1/5th your budget alone.