The thermometer should be acurate, it isn't old and is quite precise (0,2C).
As for agitation, as I said I prefer to change time not only for the habit of agitation, but also because the grain will be bigger with more agitation (you'll tell me not to use Rodinal if I want small grain... ).
Concerning the zone 0. I made the exposure test : meter a wall (zone V) and close the diaphragm 5 stops to get to zone 0. If correctly exposed, there shouldn't be fog, if I understood well. But there is some, in my case. Which means that I over expose the negative when setting my meter at 100ASA. That's why I was talking about increasing the EI.