What are the technical specifications of Tesla "cell level fuses" one fuse per cell
I was waiting for someone else to answer this who knows more, as I have forgotten most of what I once learned of the Tesla fuses.

From what I remember, they are only on the positive side.  To clear your confusion about the function of the fuses and how is so much curreng/voltage passed through the fuses - only the current from the individual battery that the fuse is attached to passes through the fuse.  That current joins with the current that has just passed through the neighbour's fuse and so on for all 74 in series and then joins the 96 groups in series, not passing through any more of those fuses you are asking about.  There are other fuses, but they are different.

The function of those fuses in your picture is to protect the 74-in-parallel batteries from a single or several batteries shorting or catastrophic failing.  For example, one of the batteries develops some sort of internal short such that it no longer holds a charge and the remainin 73 batteries in parallel see it as a piece of metal in circuit that they can discharge their entire charge into.  The fuse connecting that battery will blow and the current will stop flowing from the remaining 73 batteries, saving them from going into thermal runaway which would be the likely scenario without the fuse and you would lose the whole bank of 74 and likely have a fire.

From tests done on the fuses by a guy who disassembled a model S battery pack, they consistently blew at 25 amps.  They are not a complicated mechanism, just a thin wire than burns through at a certain amperage. 

Edit:  from re reading the blog of the fellow who took apart a model S battery pack, it appears from the pictures that the fuses are on both the positive and negative which seems a little redundant.