Alma “stretched forth his hand.” Mormon didn’t feel he needed to explain what that meant, although it would be helpful for the modern reader. Perhaps it was a gesture of formal discourse, such as was found in many Old World cultures. The orator had specific gestures that would add particular meaning to his words. In this case, it is possible that the gesture was intended either to include this group of poor in heart, or possibly as a representation of one who could speak with authority. That Mormon includes the gesture suggests that it had meaning, but we do not have enough information to know what that meaning was.
The Zoramite synagogues were used once a week for their worship service, and there was no worship outside the synagogue (Alma 31:23 notes that they did not speak of God on the other days). Thus, one of the problems these poor had was the assumption that they were barred from worshipping God. It is for that reason that Alma asks “do ye suppose that ye cannot worship God save it be in your synagogues only?”
That question is significant because it suggests that devotion to God does not require a particular sacred space. Any place can be made at least temporarily sacred if we use it to worship. Similarly, it does not matter the day. Although Christian tradition worships on Sunday, there are countries where the prevailing religion or practices make it more appropriate for members of The Church of Jesus Christ of Latter-day Saints to worship on a day other than Sunday. The worship is much more important than the day on which it takes place.