1) What would happen if one attempts to send an amount of coins to an IP address that isn't running the program?
2) What would happen if one attempts to send an amount of coins to a invalid Bitcoin Address?
Not possible, the software doesn't allow that.
3) What would happen if one attempts to send an amount of coins to a Bitcoin Address that nobody owns?
4) What would happen if one attempts to send an amount of coins to a Bitcoin Address that used to be owned, but has since been abandoned (recipient stopped running the program, or deleted their wallet)?
I guess the money will just be lost in that case.