Help me build ULTRA cheap rig(400€ and below)

Few more questions:

Was thinking of switching to HD 6670. Would the games slow down too much?

Pentium G630 - is it too slow for the online FPSes?

the intel g630 is a great low cost cpu for gaming. there are some new ib and sb g chips dropping sometime in sept 2.
stay with the 7750 it a new gpu and uses less power. there alos the 55ti and the 640/650 cards from nvdia that will play mmo online games fine. i have an i5-3450 and a 550ti and i play coh fine on my 22 inch monitor. the only thing i add is look at a mid size case (gaming) like an antec 100. or a cheap clone case
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
the larger cases are easy to work with when your putting in the mb..a few extra inches do matter. also they have right push pull fan set up already for you. micro cases are ok for webbing but if you start gaming on a min case and it does not have good airflow you can overheat the gpu and cpu. the only thing i toss in is spend a few dollars and replace the intel cpu heat sink with a good cooler that has a back plate and screws. (evo 212 or clone). the plastic leg type of the intel heat sink are a pos to lock in. a lot of users post hear that there new rig running hot..most times it the heat sink not pushed down all the way. also look to see if the one 4g ram sticks are less money then the two stick kit. most new mb will run fine with one stick.
myself i would swap the h61 for the msi g45 micro atx z77mb right now it about 100.00 us online. it let dad if he has too if a year or two swap out the slower chip for a cheap i7 and a faster gpu. (if his son still playing hard core games.)
if you need a cheaper mb then look at one of the x68 or a 6x chipset that can be flashed for an ib cpu. when dad looking at mb have him look at the warranty of them. some are real cheap on there warranty..some have 18 months. some of the larger full size mb have 3 to 5 year warranty. also when he shopping for parts see what parts are easer to rma for you where you live.
dad and his child wont be happy if they have to wait 3-4 weeks for a part.

I am using mATX motherboard and the Elite 310 is not that small case so I don't think it will be any issue. Sure, I can't do nice wirework but thats liveable. In the place where I'm buying thats pretty much the cheapest decent case.

I could not gain much from swapping motherboard. The kid will only use this cheap system for probably 2-3 years, after that if he has proven he can take care of it well, he will get something a bit better. There's no need for any upgrades, overclock or anything similar, thats why I chose cheapest platform possible for the 1155. The motherboard you suggested would cost atleast 2x times more and break my budget.

Yes, if you can.
The Phenom II 965 would be great but also more expensive.
No, integrated will not match even the 7750, although may come relatively close for the price.