Hello! You could use the word "powwow" meaning: a conference or meeting for discussion, especially among friends or colleagues or a meeting in which something important is discussed. So it could be used to describe a formal or an informal "brainstorm". For example: "My brother's getting divorced so I'm going home for a family powwow this weekend." Also, there is the phrase "bounce ideas" which literally would mean to "bounce ideas around or off each other, in a meeting." For example, "I'm really needing to bounce some ideas off you in our meeting." Then, of course, there are the more mainstream words that you could use when talking about a "brainstorming session" like "deliberate" or "problem-solve". I hope that helps!

hash out (an idea)

Your suggestions are good, as are Alex’s suggestions of collaborate and “put our heads together.” There is also “to spitball,” which means to suggest an idea for discussion. It is very informal. Example: “Just spitballing here, but what about this idea? [Then state idea.]”.

Pick the low-hanging fruit: Get the easy stuff done. That's a common one. You can collaborate, or put your heads together. Share ideas? I'm not sure what colloquial expressions I use instead of brainstorm.