Try going to the Microsoft website and see if you can use your license key to download the 64-bit version. If so, you will have to do a full re-install. If not, you will have to buy either a 64-bit OEM copy or a Retail copy that would include both versions. Either way it requires a full re-install.
The thing is, if your key wont work for 64-bit you will have to purchase a key within 30 days to activate Windows. Sometimes however a call to Microsoft might get you what you need to activate it without buying a new version (just complete the install without activating and manually try to activate via phone). If neither your code works and MS wont help, you can always reinstall windows 32-bit, which you have now. Assuming you have a Windows or system recover disc, otherwise you might want to find and make a 32-bit disc from an iso download.
No, Windows requires activation, this is what the product/license key is for. A valid key will activate Windows and you are good to go. Windows can install without activation during the install, but you wont be able to update without activation. Its the full version, but they limit what you can do after a 30 day activation grace period. If/when you try to manually activate, you call a phone number, provided by the activation wizard and they can guide you through the process. I've done it a few times, takes about 15 to 20 minutes on the phone.