The Halachos of Chewing Gum
Chewing gum raises three halachic issues:
Some poskim say that a brachah shouldn’t be said before chewing gum because it’s simply being chewed and no food is being ingested. However, the consensus among poskim is that since the one chewing gum derives pleasure and nutrition from it—as one does from eating—a brachah should in fact be said.
Gum is typically chewed while going about one’s business, often while going from room to room, or even outdoors. The halachah is that food with an after-brachah of borei nefashos requires a new brachah rishona (brachah before eating) if one goes to another room from where they can’t see the room where they made the brachah. This issue can be resolved by having in mind when saying the brachah that they may be moving from room to room; but if one leaves the house, prior intent doesn't count.
Gum is often chewed while walking outdoors. The Gemara says, “Ha’ocheil bashuk domeh l’kelev” (one who eats outdoors is likened to a dog), and is disqualified from giving eidus (testimony). Nevertheless, poskim say that one can be lenient nowadays since this behavior has become “the new normal”—but may still be inappropriate, especially for a talmid chacham. Albeit chewing isn't the same as eating, it's nonetheless inappropriate.
The second and third points apply to eating candy and ice cream as well.