One of my Tzitzis strings tore at the point where it attaches to the corner. (I have attached a picture of the spot). Can I wear it in its current state? If not, how can I repair it? Must it be restrung? Can I just tie the two ends of the broken string to one another?
It is hard to see the actual rip from the picture that you sent, but if indeed the string is severed, then the tzitzis are posul and should be taken off. You can not tie the two sides together to make it kosher because of “taaseh v’lo min h’asuy”. .What you can do is untie that whole corner, tie the two parts of of the string with a string knot, and then redo that corner of the tzitzis.
Mishna Berura 12-4, 7.