"I guess the question should be do they regard to their selves as cristians?"
Yes.
"Catholic doctrine teaches that the Catholic Church was founded by Jesus Christ in the 1st century AD and that the coming of the Holy Spirit upon the apostles signaled the beginning of its public ministry." source Wikipedia.
From what I understand, the Catholic church was the first Christian church.
Other Christian churches formed for various reasons such as the one mentioned above.
"The Bible does not have a purgatory for instance."
The Bible never calls it "purgatory", but it does talk about it. For instance, 1 Peter 3:18-20 reads:
For Christ also suffered for sins once, the righteous for the sake of the unrighteous, that he might lead you to God. Put to death in the flesh, he was brought to life in the spirit. In it ( it being death ) he also went to preach to the spirits in prison ( prison being purgatory ), who had once been disobedient while God patiently waited in the days of Noah during the building of the ark, in which a few persons, eight in all, were saved through water.
I added the emphasis ().