Addressing these in reverser order:-
2) Yes - different I/O banks can be powered at different voltages.
1a) Yes. You can power one (or more) bank(s) at 2.7V.
1b) The impact on 'performance'. This depends on what you compare it to. Altera (and Quartus) characterise I/O performance at the discrete voltages specified in the datasheet. Quartus will ask you to specify what I/O standard your pin is operating at. You'll end up having to chose a 2.5V or 3.0V I/O standard. So, Quartus will qualify your signal based on the I/O standard you chose and an assumption that you're powering the bank accordingly. So, when you power the bank at a different voltage the above assumptions are invalid.
Does this matter? This depends on what you're trying to do and will largely depend on what speed you're expecting to run the interface at.
Before powering a bank at 2.7V, you should also consider powering it at 2.5V or 3.0V anyway. Check the minimum voltage each end of the interface will generate for a logic 'high' and qualify the link for yourself. Driving 2.7V into a bank powered at 2.5V will cause you no issue, but will the other end always see a 2.5V level as a logic high? Power the bank at 3.0V and decide whether your 2.7V device will always meet the minimum FPGA threshold for a logic high. Perhaps your other device will happily tolerate receiving a 3.0V from the FPGA. If not, depending on the frequency of you signal, you could condition it externally - with a buffer or simple pot-down resistor network.
Cheers,
Alex