I recently purchased a Diadora Orbita bike from SportChek. As I was riding it my front derailleur got bent and now I can't use my pedals. So, my question is, can I remove the Shimano FD-TY18 front derailleur without unlinking the chain? I don't have a chain breaker, so my only option seems to be to remove the derailleur without unlinking the chain. Is it possible?
The pictures I've found of the FD-TY18 look like the pin across the rear of the cage is riveted in place. So, you probably can't remove it without a bit of work – through if the derailleur is damaged beyond repair it probably won't be too hard to either pry it apart (try holding with a screwdriver and twisting one side with pliers) or to cut it (and do double check that there isn't a screw there).
But before you do all of that, check your chain carefully. Many chains these days are connected with a master link which makes it easy to split the chain without special tools.
Get a good cutter and slice the derailleur cage. (Without a picture can't say it for sure, but I bet your derailleur isn't repairable if it bent so much that it prevent your crank movement).
If you've got a Shimano chain it's unlikely that you've got a master link as most Shimano chains come with a one-time use connecting pin. You can pop this back out with a chain tool. It's not practical to easily remove it without the tool. You can replace with a kmc missing link (make sure you match it for the right chain) for easy disassembly in the future.
6/7/8 speed chains may just use regular pins which can be manipulated carefully with a chain tool and pins can be reused if not pushed completely out.
If the derailleur is riveted closed, you won't be able to take it off the bike without breaking the chain or destroying the derailleur. If you're going to replace it, then you'll need to break the chain anyway to put the new derailleur on. So if that's the case, then just buy a chain tool and new derailleur.
However, if you're willing to play with it a bit, you might be able to bend the front derailleur cage back in to place. Use a pair of needle nose pliers to flatten out any kinks and try and bend it back to the right shape. I've done this a couple times after some poor footwork had me kicking the front derailleur cage. It may work, it may not, it may take some tweaking, but it might save you the hassle of replacing it (or at least make your bike rideable till you can get it fixed proper). No guarantee this will work in your case as I'm not sure how bad the bend is.
If you can't ride without chain rub after trying to bend it back, you're better off replacing the front derailleur. Get a bike shop to help you if you don't have the tools.