No need to go 3mm - on a flat cutting table most sheet materials I find I can get away with 1mm, with plywood requiring 2mm as it is never truly flat.
According to the COSHH sheets, European MDF isn't toxic at all, and hasn't been since about 1995 when the E1 standard was introduced. AFAIK that effectively ended the use of resins containing formaldehyde on the production of MDF.
@petermillard did a YouTube video about MDF toxicity which you might find of interest
You do well to wear a mask, but is your mask up to it? At work (construction) we mandate the use of face-fitted P3 masks when cutting MDF, chipboard and plywood together with an L-class or M-class vacuum depending on what is being cut.
In a home environment you obviously won't be able to do a full face fit test (which requires a test rig and a trained tester) but if you are relatively clean shaven you could opt for a JSP Force 8 mask with P3 filters (AFAIK the only mask to feature a seal self test facility), or if you are whiskered then the obvious choice would be an air cap or air helmet of some description which blows filtetedcair down over the face (but can be a bit cold in winter), again with P3 filters. In terms of vacuums, most home vacuums or shop vacs aren't up to the task of filtering MDF dust, but if you can't run to an M-class vacuum, you can get near to the same effect by fitting a pre-filter cyclone between your tool and the shop vac
It depends. About 20 years ago the OSHA in the USA did some research which concluded that the dust from western red cedar is carcinogenic...
And whilst it may or may not be carcinogenic, the formaldehyde in softwoods as well as the resins can lead to a form of allergic rhinitis - something I know about from first hand experiencr