I bought a Dell U2713HM because it was highly rated and had 2560x1440 resolution, but, after learning that the HDMI connection only provides 1980x1080, I purchased from Apple their Thunderbolt to DVI connector and tried that. Still 1980x1080. I've now ordered a mini-DisplayPort-to-DisplayPort connector and am praying that I get the full resolution that way, but I've seen a number of user group comments that you need a completely separate (over $100) Thunderbolt data (not display) interface to get the full resolution. If that's true, I'm returning the Dell. I've also seen people say you need to reset the PRAM and SMC settings, but I've tried doing that (I think it worked) but nothing changed.
I don't think an ordinary DVI connection would be enough to reach a 2560x1440 resolution. For that you'd need a dual-link DVI connection, and in your case a mini-DisplayPort to dual-link DVI converter like this one. It costs $99, but you could probably get a generic Chinese clone on DealExtreme or eBay for much less. I can't speak for the mini-DisplayPort to DisplayPort converter as I'm not familiar with the DisplayPort standard.
Dell supplied their monitor (at least my U2312HM) with DVI Single Link cable. That's the reason why you have incorrect resolution and frame rate.
To get higher resolution you need to buy DVI Dual Link cable (with 9 additional pins) to get support higher resolution and frame rate.
I sure that Dell made a mistake to supply the monitor with DVI Single Link cable.