Hilchot Spinner

Is a Spinner Nonsense
Q: Some claim that the new "Spinner" is nonsense and therefore one should refrain from letting kids play with it?
A: Almost all games are nonsense, but kids need to play.  Every person needs to take a bit of a break (See Rambam, Shemoneh Perakim Chapter 5), and this is all the more so true for children.  The essense is not to overdo it.  Although there are smart games, such as Chess, kids also need easier games.  In sum, it is no different than any other game, and one should not over do it or become addicted to it.

Girl Playing with a Spinner
Q: Is it permissible for a girl to play with a spinner while walking in the street or does it draw unwanted attention to her?
A: It is permissible, since many play with it and it does not especially draw attention.

Spinner in a Shul or Beit Midrash
Q: Is it permissible to play with a spinner in a Shul or Beit Midrash?
A: In general, a Beit Midrash is holier than a Shul. The reason is that in a Shul, we turn to Hashem in prayer, but in a Beit Midrash, Hashem turns to us through Torah learning.  It is therefore permissible to turn a Shul into a Beit Midrash, but not visa-versa, since we go up in holiness and not down.  Nonetheless, there are more leniencies regarding a Beit Midrash since a person spends much of his time there and it is his home.  In a time of need, one may therefore eat and sleep there.  This leniency also applies to other acts which are not Torah learning and prayer on condition that they are not acts of frivolity.  See Shulchan Aruch, Orach Chaim #151.  It is therefore permissible to play with a spinner in a Beit Midrash when one needs it for concentration, but this is forbidden in a Shul.  If one claims: but it helps one concentrate during Davening?  We are not in Shul for so long, and a person can concentrate for this amount of time without it.

Playing with a Spinner during Davening and Torah Learning
Q: It is correct that it is forbidden to play with a spinner during a Torah class, Torah reading and Torah learning?
A: Correct.  Absolutely.  One needs to have awe of holiness.  Berachot 22a.

Spinner on Shabbat
Q: Is it permissible to play with a spinner on Shabbat?  Is it forbidden on account of "Refuah" (medicinal purposes) since it is meant to help people with issues of concentration?

A: 1. If it has lights, it is forbidden on Shabbat.  2. If it does not have lights, it is not forbidden on account of "Refuah", since it is not recognizable as such.  3. It is considered like any other a toy, and is thus permissible for Ashkenazim and an issue of dispute among Sefardic Poskim.  See Shulchan Aruch, Orach Chaim 308:45.  Mishnah Berurah 338:21.  Yalkut Yosef - Shabbat Volume 2 308:6.  Shut Or Le-Tzion Volume 2 26:8.  4. If one can take it apart and reassemble it as part of a game, there is no problem of building.