打招呼 To call out a greeting. Also to tell someone about a matter beforehand or afterward, or to remind them of it.
吹风 To blow wind. To let information out, or to make an opinion known.
通气 To let the air through. To keep each other informed.
摸底 To touch the bottom. To find out the real situation and the inside story.
探口风 To probe the wind from the mouth. To sound out what another person thinks. The Handian dictionary’s example comes from marriage. Instead of proposing a match, the other side first sent someone to “throw a stone to test the road” and sound things out.