How can I simulate x6500 or x6000 FPGAs?
You need an HDL simulator.  Icarus Verilog or GHDL are two opensource options (one for Verilog and one for VHDL, depending on what language your source code is written in)

With the simulator you can examine (veeerrrry slowly compared to the actual FPGA) what goes on inside with full visibility of the internal signals.

However, you are not likely to break the board just with code - as long as you treat it carefully with regard to keeping high voltages off the pins (nothing > 3.3V), take reasonable precautions against static zapping it, a well-designed board will take any code you can throw at it without blowing up.  Heat may be a potential problem, but usually the code stops working as the chip heats up (and usually it stops heating up then as the logic stops toggling as it's all confused and the state machines tend to lock up).  Stick a big heatsink on it or some temperature sensitive labels if you are worried.