You do have a pair of early Hardinge Cataract machines. Google Tony Griffiths Engineering. He shows a huge number of machines. Among them are your lathe and milling machine. You can see what the missing "jockey" pulleys look like. Tony is the best resource there is. I took a long train ride to visit him some years ago. He sells Myford lathes,and other smallish English machines.
He also sells excellent reprints of many,many manuals. Your machines might be included. But,be prepared to spend over $100.00 for manuals. They are very well done,though. I sends him old manuals to help him when I can lay hands on them.
I have a lathe just like yours,without the compound. Have had it for years. I ought to sell it as I'm probably not going to get around to putting it together.
Those lathes were used for accurate tool room use,and making master plates for clock making. They are featured in the book "Precision Hole Location",which I have an original copy of. A lot can be done with those face plates you have.
Tony's site shows how the lathes were powered by small overhead belts. The mill was powered from under the table,I think. Study the pictures and text he gives. Much will be revealed.
Threading on many early lathes was done with special threading tackle. You will see those too. Keep searching his list for other early brands too. I have read every single machine he lists,spending many hours at it.