Can wearing a face mask give you a fungal lung infection?

If you wear your mask long enough to cause some weird fungus to grow on the mask - maybe.  But a person would have to knowingly wear a stinky, moldy mask to be at risk.  Most people would not do something that stupid.

Yes. Especially if you have to wear it for extended periods of time.

No. Many people wear masks all day long for work and none get fungal pneumonia 

Not if you clean your mask and  replace the mask  regularly.  Depending on your work are  it helps with my allergies a little.