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Is it possible to change my present WordPress site or do I need to start from scratch?

What do you mean by "change"? Change the theme or delete everything, edit the theme and start over?

If I buy a domain name the way you described can I change my present site into that one? If not it means all my articles are lost or?

Yes, there is a way of connecting the present server with another domain, but I don't know how to do it.

I will figure that out first. Thanks.