Sentence number 1 and sentence number 3 are correct. Sentence number 1 states what he is doing right now. Sentence number 3 states what he does regularly or habitually. Sentence 2, sentence 4 and sentence 5 are all wrong because there is no article ("the" or "a") before the countable noun phrase "mask" or "fabric mask".

They’re both correct, but it depends on the context. If only one were correct, it wouldn’t matter, since the meaning would be clear. The purpose of having different verbal aspects is to allow us to communicate more information. If you say “for the first time” (as you did in your original question), then it’s probably (but not necessarily) the continuous aspect. You may benefit from reading my article on the topic: https://www.italki.com/discussion/205633

So #1 is more like he is wearing a mask RIGHT NOW. I can see that he is wearing a mask, or I know he is wearing a mask. Example: You see your dad leave the house with a mask on but your mom did not. Your mom: Did he leave the house without a mask? You: He is wearing a mask. And #3 is more of a hypothetical or situational answer. In which, even if you don't know if he is wearing a mask right now you know that he wears a mask to cover his face when he goes outside. Example: Your friend ask what your dad does to protect himself when he goes outside. Friend: Does your dad put anything on his face when he is outside? You: He wears a mask. (see this time, you don't know if your dad is wearing a mask right now but you know he normally wears a mask when he goes outside so you say he does.)

#2 and #4 seem to be missing an article before 'mask'. I can not imagine a correct use of them. #1 describes a present event or something current; #3 is a general staement whihch might refer to usualy actions of this person.