Hi!
From my experience as violinist wich I still are :) I can say that:
- The lower information is an alternative. Wich you use depending on your likes on interpretation. Basically, because the same note in different position and string sounds quite... diferent.
- Digits for Finguers.
- Roman numbers for Strings.
- In doble stops, it is normal to have the upper digit for the upper note and the lower for the lowers note ;) but these are writted toguether, not up and down the system but in the same line one over the other in a fraction way (like the time signature)
In your image of the Bach violin concert, you pass over a 3 and 1 fingering posibility after the reharshal mark C at the b note.
What it sais is that you can play the b note at the II string with finger 1 wich gives you the note in first position, or you can play it with the 3 finger over the III string arriving to the 3º position.
Since it had not string indication, one can be crasy enough to try and play with finger 1 on the III string ;) wich gives you the 5th position, probably a nice sound and probably an awfull way back to confort :) Just for fun!
There are plenty of posibilities.
It seams that the editor, aparently in a way of trying a clear view (because he didn't had Lilypond) decide to omit the number of the string, so it doesn't overlapp with the p (piano) symbol.