External display works on 30Hz

No, it won't support it. The Thunderbolt 1 controller in the Air only supports DisplayPort 1.1 and you need DisplayPort 1.2 to get 4K support, as you mention in your question.

Check out http://www.anandtech.com/show/7049/intel-thunderbolt-2-everything-you-need-to-know and http://en.wikipedia.org/wiki/Thunderbolt_(interface)#Thunderbolt_2

Short Answer:

Yes you can run a 2560 x 1400 @ 60Hz on an external monitor. Thunderbolt compatibility doesn't matter since the only interface you need to and can work with is the mini display port (mDP).

The question now is, what are your "goals?" Maybe we can direct you to a different solution.

Background

The MBP Mid-2012 only came with 512MB VRAM, not the 1GB you are specifying. In any case, the maximum resolution you will ever get will be 2560 x 1600 MacBook Pro (13-inch, Mid 2012) - Technical Specifications

That said, there is no "thunderbolt to display port" adapter. Below is a snipit from another answer where I addressed this very issue:

Now, there is no "Thunderbolt" to DVI/HDMI because Thunderbolt is an extension of PCIe. So, in a very basic sense, this would be like trying to plug your monitor in directly to the logic board and not go through the video adapter; it cannot happen.

However, Thunderbolt "multiplexes" the DisplayPort signal on that single cable. You are going to get both. Now, if you use a a Thunderbolt compatible cable, you can daisy chain additional TB devices off your monitor, albeit at a reduced data transfer rate. This is why monitors are the last in the chain. If you use a non-TB cable, you will only get display and no TB signal.

The mini display port (mDP) on your MBP isn't going to give you any more resolution than your GPU is capable of delivering. mDP 1.2 can support up to 4K video at 60Hhz; it's just your MBP can't deliver it. Changing your cable to one that supports more bandwidth isn't going to give you more resolution the same way changing out your cat5 cable for cat6 will increase the bandwidth of your 1GB NIC.