How can I chat with BlackBerry users? Is there an app that lets me chat with BlackBerry users just by adding their PINs? Something that simulates that my Android phone belongs to the BlackBerry network?

I know there are multiplatform options like WhatsApp but I am talking about an app that lets me chat with people who are using the native BlackBerry Messenger.
You can't.  RIM's PIN system and BBM are proprietary.  You can only communicate with a BlackBerry user via PIN messages or BBM if you have a BlackBerry.

Get a new Bold 9900 / 9930, they're great! Full disclosure: I work for RIM. This is not an official statement from RIM either, this is me speaking as a user in my off time at home. I honestly think the new Bold is the best BB yet.