Subject-Verb Agreement

I'm working on an exercise that calls for identifying whether the subject and verb are in agreement (or if they're not) and to identify the simple subject of the sentence. There's a few about which I'm puzzled and I need some clarification.

"Neither the project manager nor the supervisors has been informed of the cancellation of the job." (I said that has should be have. Now, would the simple subject of this sentence be manager or would it be a compound subject, featuring manager and supervisors? My textbook keeps identifying the compound subjects in their examples, saying nothing about what to do for simple subjects.)

"Every team member and project leader are recognized for his or her efforts." (I said the verb should be "is." Is the SS member or leader, or is it again a case where it's both, functioning as a compound subject?)

"Having access to technical personnel and support are a major concern for our project support group." (I said are should be "is." SS = access, yes?)

"Trimedics bring key people together and make them responsible for specific customers or for certain product lines." (I said bring should be "brings" and make should be "makes." SS = Trimedics.) Yes?

"Brainstorming was the major source for our team's solution to the problem." (I said this was in S-V agreement, with SS = brainstorming. Correct?)

Thank you to those that can help!