Ok, so I went for downloading again Cross Fingers, and play once more this gem! I put my password in and, bam!, the icon of CF appeared and disappeared after a second, downloading nothing...I tried with another game...nothing to do...same thing. It seems I can't download any game directly from my iPhone! Luckily I can download games from iTunes on my PC and pass them to the iPhone...but would know if anyone else has the same problem!
App store is ok if you browse using an iOS device, for all those with problems browsing on a Mac or pc.