According to many poskim, a minor who kept up-to-date with the sefira count and became bar-mitzvah during sefira may continue to count with a beracha. This is also the opinion of several contemporary poskim: Rav Shlomo Zalman, Rav Shmuel Wosner and the Or Ltzion. Other contemporary poskim -- Rav Nisan Karelitz and Rav Chaim Kanievsky -- say that he may only continue to recite the beracha as chinuch, and as such he cannot exempt an adult with his beracha. According to the Avnei Nezer, he may not continue counting with a beracha.
(??????? ??????? ????, 79)
Hilchos Tzitzis 12 (page 48)
Wearing Tzitzis in a Reshus Harabim on Shabbos
Wearing a Garment Without Proper Tzitzis on Shabbos
Wearing a Garment That is Less Than the Shiur on Shabbos
Wearing tzitzis in a reshus harabim on Shabbos
On Shabbos it is permissible to wear a talis gadol or talis koton in a reshus harabim. The strings are not considered a 'forbidden load.' On the contrary, they are considered a necessary component and an adornment to the garment. They are considered part of the garment even at night (when the mitzva does not apply) and when the tzitzis are required only mid'rabonon. The talis must be worn in the typical manner in order for the talis itself not to be a 'forbidden load.'
Wearing a garment without proper tzitzis on shabbos
A garment that has some
tzitzis but lacks the proper amount to be kosher (some strings were never put on) may not be worn mid'oraisa in a reshus harabim and mid'rabonon in a karmelis (see Shulchan Aruch 345:14) on Shabbos. In this case, the 'kosher' strings are not considered just a part of the garment since they have their own importance as mitzva objects. Another reason they would not be considered batul to the garment is that they are still in the process of being completed. If the strings had once been kosher but tore and are no longer valid (e.g. they are all too short), the remnants are batul to the garment because they are useless.
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Wearing a garment that is less than the shiur on shabbos
According to some poskim, a garment which is smaller than the necessary shiur (see 15:1) and has tzitzis may not be worn in a reshus harabim or karmelis on Shabbos; since the strings are not fulfilling a mitzva, they are not considered part of the garment. Other poskim permit wearing it like this, reasoning that when the wearer intends to appear as if he is wearing tzitzis, the strings become part of the garment. According to some poskim, a child may wear a talis koton which is less than the shiur on Shabbos.
(?"? ?; ??????? ??????? ????, 1)
According to Rabbenu Tam, torn tzitzis remain kosher only if they are still kdei aniva and at least two of the four [doubled] strings are intact.
According to the Mechaber, the halacha follows the Rosh's opinion -- though when possible, it is proper to be stringent like Rabbenu Tam. According to the Rama, the halacha follows the opinion of Rabbenu Tam.
According to Rashi, the kdei aniva must be on the loose part of the strings. According to the Ri, it can even be in the braided section of the tzitzis. It is proper to follow Rashi's opinion in this matter.