I'll accept that some forms of written submissions might be regarded as advocacy, but other than that the areas you mention above either aren't advocacy in the true sense of the word, or it doesn't fall within Counsel's area of expertise:
- negotiation. Its rare to get Counsel involved in face to face settlement negotiations, save for where Counsel speak to their opponent at the door of the court.
- mediation. Again, rare for Counsel to be involved. Mediation works best when legal issues are left to one side.
- arbitration is, to all intents and purposes, court advocacy in a different forum.
- the preparation of witness statements: again, Counsel might be involved in settling these but I wouldn't regard this job as being "advocacy".