If I build and simulate a project using Quartus Prime Lite Edition, will it be compatible with Quartus 2? Will the simulations work properly?
Quartus II (not 2) was what older versions of the tool were called. If you take a newer project into one of those older versions, you'll need to recompile the design (same if you take an older project into a newer version of the software) in order to synthesize and run it in hardware.
For simulation, are you talking about using the old built-in simulation tool or a separate tool like ModelSim-Intel FPGA Edition? You really just need source design files and a testbench file to simulate.
So i actually don't need to synthesize my designs, it's just for simulations (educational purposes). My aim is to use Quartus Prime Lite edition, which is what I have available on my computer, to build my project and simulate it. However, since my instructor will be using Quartus II, I need to confirm they will be able to re-compile and simulate it.
And for the simulator, I'll be using ModelSim-Altera.