What type of camera is this? And model? Brand?

This is not a "here" rule, it's a whole Internet rule.

 

What would be equivalent today as the Sony R1?

 

The R1 was made in 2005 - 2006. Available used.
It was considered a Bridge camera, and had a 10megapixel APS-C sized sensor.

It's really nothing special today. A mid-level camera though it was the first time a APS-C sensor was used in a bridge camera (just read that on Wikipedia).

A bridge camera is a "class" of camera between a Point and Shoot and a DSLR type camera.
Many Mirrorless, DSLRs, bridge cameras have APS-C sensors.

So it's hard to give you an equivalent today .. other than nearly ANY bridge camera. or ANY APS-C dslr camera. or ANY mirrorless camera that has an APS-C sensor. Of course any thing new would have a larger megapixel sensor.

or just go to the Sony website and look at bridge cameras for the most equivalent in regards to historical connection.

The problem is ... no one here understands what is "special" about that camera to take a certain photograph as ANY camera can do that.

 

A Sony R1. You can buy a used one on ebay.


Once again: What is so special about this camera? Why do you think it has special abilities? What ARE these special abilities? Is it the flip-up screen? Is it that it looks different than a 'traditional' DSLR? Is it it's rarity? That it's no longer made?