Hi Kina, regarding the iPhone contact groups, yes: I made them with copytrans contacts. If you want to create contact groups on your iPhone, run the program on your computer, connect your iPhone, then right-click within the Contacts pane and select "New group" giving the group a name:
I do not have an Android device but am almost sure copytrans contacts is only designed for Apple iDevices. If you already transferred your old iPhone contacts to your PC, you can transfer the contact entries to your Android phone's SD card and then import them from there after having installed the SD card back on the phone.