Ferric chloride, if heated, will release HCl. It is unlikely your respirator will block that, unless you have something with activated carbon. In this day and age it is impossible to tell someone not to take a safety precaution. I do not and have never worn a respirator when dealing with ferric chloride indoors or out. Your material is in solution as well. That reduces the risk from the dust considerably. Eye protection is important. Be sure not to omit that.
As for disposal, just consider that the major use of ferric chloride is for sewage and water treatment. It is also used in many areas to kill roots that invade sewage lines. The risk in sewage is not from the ferric chloride, but from the copper salts that are produced during etching. To that end, I minimize the amount of copper that is removed by using copper pours.
Finally, ferric chloride etchant will last a very long time. There is no need to dispose of it after each use. I use cupric chloride (similar chemistry). It never wears out and never has to be discarded, unless the volume gets too great. Ferric chloride can equally be reused. It will eventually turn into a mixed cupric chloride and ferric chloride bath after a lot of use.
John