Yes, if the Hazmat suit includes a mask (i.e. covers the face).

does it apply to Everything that you put on your face?

If it covers mouth and nose, it'll give some protection, e.g. a bandana gives 25% protection, a surgical mask give 50%. Only a proper gas mask gives full protection.
Balaclavas and halloween masks on the other hand offer no protection.

What about a dust mask? I'm asking because I couldn't see this asked anywhere else, additionally, there's no visible protection value and I don't want to risk my character :D

Please ignore my question I just noticed the mask list and it's literally the first item

Shouldnt the dust mask be more than 50%? It looks like it's n95 style... which is 95% ...then again it depends what it is we're filtering here...