Why does Altera DE2-115 board GPIO expansion header contain 5V & 3.3V power but the IO standard has no 5V?
The FPGA doesn't use 5V, but some of the other parts on the board might. (The HD44780 LCD they're using often requires 5V on VCC, for instance.) Since it's there, they might as well provide it on the expansion connector in case you find it useful.
Absolutely not. The clamp diodes are a last resort, and are only intended to protect the FPGA from brief overvoltage. Connecting a 5V output directly to a FPGA pin will cause a large current to flow through the protection diode, destroying it.

Some development boards I've seen use small (e.g, 100Ω) series resistors on FPGA I/Os to limit the current through protection diodes. This limits the speed of these I/Os, though, and I would not recommend that you rely on this for large level shifts, like 5V to 3.3V.

Bottom line: if you need to interface a 5V-only part to an FPGA, use a real level shifter. A 74LVC245, for example.