PCB design for Cyclone III 144 pins

FPGA PCB design isn't essentially different from general high speed digital design.

You'll start with selecting a layer stackup and PCB technology (particularly trace width and clearance) according to technical requirements, acceptable costs and local availablility. Power supply and bypassing should be planned in advance. Don't forget to connect the enhanced pad of the EPQF package.

I don't know what you exactly mean with "mapping of IO banks". I guess, you have seen schematics with separate symbols for IO-banks?

Usually some manual action is involved to transfer pin assignments between Quartus and the Cad tool. This isn't a big issue for a small 144-pin package, you'll possibly want to automate the process when working with 484 or 976 pins... In any case, the pin mapping should be validated in Quartus before making the PCB.

It's often helpful to assign pins according to routing requirements, particularly with 4-layer or even 2-layer boards.