May a child wear a Tallis Katan with torn strings? Must the Tzitzis of a child be Kosher, as is required by the Tzitzis of an adult?
Children of all ages may only wear a pair of Kosher Tzitzis. Thus, if the Tzitzis tears in a way that invalidates the Tzitzis, the child is to no longer wear it or say a blessing over it. Nevertheless, some write that until the age of Chinuch [age 6] one may be lenient to validate torn Tzitzis so long as they abide by some opinion mentioned in Poskim.
See here for the full details of a torn string: https://shulchanaruchharav.com/halacha/strings-that-tore/ and https://shulchanaruchharav.com/halacha/a-single-string-tore-is-my-tzitzis-still-kosher/
 See Piskeiy Teshuvos 17:2
 Thus the strings must only reach a length of 8 cm [opinion in Michaber 11:4], and may be torn on all sides so long as Kdei Aniva remains, and so on and so forth.