Does wearing a mask make your lungs stronger like high altitude training?

No, and higher altitude doesn’t make lungs stronger. It does increase red cells which carry oxygen bound to hemoglobin, you lungs do gas exchange the same as at low altitudes.

A training mask is designed to help you re-create the conditions of high altitudes when you can't physically go high above sea level. ... When you wear the mask, your body begins to adapt to the reduced oxygen intake, making your heart and lungs work harder.

Yes, because one needs to use a little more force to draw in a breath.  So wearing a mask has additional benefits besides limiting viral transmission.

It makes no difference. Unfortunately wearing a mask will not qualify anyone to climb Mount Everest. 

Yep, we need now to practice for we are going to Mars sooner, bcoz mother Earth is dying.

I would think so. I gasp like i was climbing a mountain every time i shop for groceries.