Speak
Like "say," the word "speak" refers to thoughts and feelings moving from our more internal spiritual levels to our more external ones -- and ultimately from the Lord, who is in a sense the most internal spiritual level of all. This is generally called "influx" and "perception" in the Writings, meaning they are thoughts and feelings that flow in in a complete way from the Lord, rather than being things we have to think about and figure out. On a number of occasions "speak" and "say" are used together; in these cases "speak" refers more to intellectual instruction in matters of thought and "say" refers more to feelings and affections that flow in directly.
Gate
Gates" in ancient times had a significance that does not hold in the modern world. Cities then were enclosed by walls for protection; gates in the walls let people in and out to do their business, but were also the weak points in the cities' defenses. In the Bible, cities on one level represent the minds of individual people. On a broader level, they represent beliefs shared by a community. The gates, then, represent openings where the Lord can feed us an understanding of truth and a desire for good. They also represent points where the hells can invade and sway us with false ideas and evil desires. We are kept in balance during our lifetimes, with influences from both the Lord and from hell. Ideally, we will over our lifetimes continue to invite the Lord farther and farther in and drive the hells back until ultimately the Lord can occupy our minds completely. And that point our belief in Him and His power and love will hold the gates and deny evil any entrance. As individuals, we at that point become angels. As communities, we at that point become part of the Lord's church. And at that point the gates become an entry point, introductory truths that allow people to enter churches and start bringing the Lord into their lives.