The levers are Shimano BL - R550, widely available for around GBP 15, and designed for calipers. The cable pull with the calipers is quite short. It is the V brakes that need the longer pull because of their greater leverage, but you can get levers like this with a two position cable end holder, so they can do either.
Yes, the 6 speed block was the original narrow one, the 7 speed ones are fat enough to fit modern 130mm drop outs and fill the same space as a 9 speed at least. The Alvio derailleur is the highest spec you can go in Shimano to get the correct shifting on the more widely spaced 7 speed freewheels. Above that spec, the parallogram is different, although they do work OK.
Yes, the 6 speed block was the original narrow one, the 7 speed ones are fat enough to fit modern 130mm drop outs and fill the same space as a 9 speed at least. The Alvio derailleur is the highest spec you can go in Shimano to get the correct shifting on the more widely spaced 7 speed freewheels. Above that spec, the parallogram is different, although they do work OK.