1) is there a way to find out if it has been softmodded or if it has a chip?
Put a backup in and try to play. If it does play, your Wii is modded (chipped or softmodded with disc channel mod). If you have the Homebrew Channel, Gator Backup channel, chances are you're soft modded.
2) which in your opinion is better?
I have both. I like both. Softmod allows me to play games from a hard disk now, so I'm leaning toward softmodding. If you don't have brick protection, and your Wii is bricked, a chip gives you more options in unbricking it.
3) Are the amount of backed up games you can play limited depending on how old the chip is?
Chances are, you will be able to play all the games you want to. Compatibility is generally not an issue.
4) if i do have a mod chip, how do i find out which mod chip it is?
I would crack it open and look at it. Others may chime in on other methods.