It seems that there is some merit to the claims.
https://www.health.harvard.edu/diseases-and-conditions/what-to-know-about-methylene-blue
None of the things the OP is inquiring about taking it for have been verified. Perhaps the last sentence of the referenced article makes the point:
"It’s critical to keep in mind that just because a particular drug or supplement works in a highly specific clinical setting (like breast cancer detection), that doesn't necessarily mean that it can or should be used by the general population."
The MN Science Museum has a great exhibit from older times on things like this. https://new.smm.org/exhibits-experiences/weighing-the-evidence
Of course, that assumes that one trusts science and not the words of only their particular echo chamber of choice...