What are the 3 elements of architecture?

oh... hard to say. It's a good question.

It depends on what you mean by type. There are types by historical period, by geographic area, by function, etc. One thing's for sure, there are more types of types that ever before. At least hundreds, because some types are subsets of other types.

By "...are there?", are you talking about what's presently being designed and built, or what is still around (hasn't crumbled), or the sum total of what we have some knowledge? Same thing, at least hundreds.

Architecture is like clothing style. There are more styles of clothing, fashion, and fabric than ever, but not all are still in use. Almost no one dresses like a Druid priest anymore (and very few did, when they did, thousands of years ago) and almost no one designs and builds residential flats like those found in southern Turkey centuries ago.

The good news; More "types" are on the way, so more choice. Also, types tend to reflect the values and beliefs of the architect and the client. So, in a way, there are as many types as there are architects. It's an exciting time for architects, and for those who live in those architect's creations.