Welcome to the forum. With razors you will likely never know the date of manufacture, only an approximate span of years it may have been made in. You may find the model from old catalogues and sources like that. Yes, it is carbon steel.

The Boker tree symbol has changed over the years so you may be able to match the tree symbol on the razor to the same design found here STRAZORS.com - all about classic razors - H.Boker & Co, Solingen. to find a time period.

Bob