I have a Lexmark printer which is a little old. So when i connect my iphone to it via the USB cable my printer doesn't recognise it. If i bought a bluetooth adaptor for the printer would i be able to print photos via bluetooth?

The only way to print from an iPad is to have a printer that supports AirPrint. Here's a link to an Apple support page on AirPrint.

http://support.apple.com/kb/ht4356

AirPrint is way to print wirelessly via Wi-Fi but it requires that the printer supports AirPrint. The iPad cannot use Bluetooth to print and it will not print when connected via USB.

The iOS Bluetooth profiles do not support attachment to devices like printers...only direct printing mechanism is to an AirPrint enabled printer. There are apps in the app store that will allow printing to a printer on a wireless network.

No.

You needs to have the printer on your home network. I use print direct to print to my non-AirPrint printers. There are others in the App Store.