Do we each need an attorney? 
I strongly recommend that both divorcing spouses consult an attorney of their own at least once during the mediation process. At minimum, I would urge you to ask your respective attorneys to review any proposed Settlement Agreement before it becomes legally binding. Attorneys functioning as mediators are not allowed to offer legal advice of any sort because it would constitute a conflict of interest. This means that even if your mediator is an attorney you should still strongly consider seeking outside legal advice.
In mediation, the role of your individual attorney is typically that of an outside consultant who is utilized for legal advice on matters that may be pertinent to your situation. For example, an attorney can discuss your legal rights, develop proposals and counters to offers by your spouse, and suggest potential best-case and worst-case outcomes if the dispute were contested in court. For some individuals, a single consultation towards the end of mediation to review the Settlement Agreement is sufficient. Others, however, prefer to consult with their attorneys more frequently. There is no right or wrong way to utilize an attorney; it depends upon your comfort level and what you perceive your needs to be.
Your choice of attorney is actually more important than the frequency of consultation. Many attorneys believe strongly in the benefits of mediation, but others see mediation as a threat to their business of representing clients in litigation. A mediation-friendly attorney will be happy to consult with you on an hourly basis rather than demand that you retain him/her to represent you in litigation.
We really don’t want to involve attorneys. Can we avoid them entirely?
As mentioned above, I strongly advise my clients to each seek legal counsel, however doing so is not a requirement for mediation.
Should our mediator be a practicing attorney?
Your mediator should be a professional mediator who has completed a formal training program in mediation. I have a bias towards mediators having a strong background in psychology or communication because a successful mediation depends so strongly on those factors being recognized and handled in a skilled fashion.
While there are a number of attorneys who are mediators, please keep in mind that mediation is distinct from the adversarial process of litigation in which attorneys are trained. Mediation is a communicative process, not a legal one.