Yes. No. Yes. No. Yes. Spandex and regular clothes can have some protective qualities but that’s not why superheroes wear spandex.
The thing with protection and in order to properly estimate how well something will protect you – you need to know what you’re protecting against. Depending on the hazard and the situation, a little cloth can work wonders.
Re-enforced clothes like Battle Dress Uniforms can protect against environmental hazards (such as thorn bushes, gravel, etc), light shrapnel, chemical agents, detection via infrared, low heat flames, etc. They won’t save your life immediately but they’ll protect against pain, shock and infections. But you’ll still want to wear armor over the top if you expect to get shot at.
Leather can be really protective (hence why it’s considered standard motorcycle gear) and also has potential for lots of re-enforcing. They’re expensive, but you can get bullet armor that will protect against the vast majority of pistols – and still look like an old school biker jacket.
Spandex and similar products are not particularly tough against say bullets, knives or fire. In fact the main thing it’s advertised as protection against is sunlight. Spandex-like wet suits are often made to protect against chill, wind, sun even being weighed down by water.
The reason that superheroes wear them is not for any protective quality but rather that they allowed artists to showcase the super heroes as having larger than life physiques and being demonstrations of perfection. While his physique doesn’t seem unattainable now, Superman started in 1938, and this is what a contestants in the 1953 Mr Universe competition looked like:
(If he looks familiar, it’s because he’s Sean Connery)
Basically the problem with the double standard is that superheroine designs are less about looking like the perfect powerhouse and more about looking like the perfect sex toy. To the extent it’s hard to take them seriously and people spend no small amount of time pondering the hazardous of the outfits.
There’s also the matter that creators are often quite comfortable loading up heroes like Batman with so much armor that he needs servos to run and jump around, but heroines like Batgirl are always limited to what can show off her silhouette and show the exact shape of her boobs.
Designs don’t necessarily need to be protective, particularly if you’re selling a larger than life power fantasy – but it shouldn’t look like it’s a massive liability purely for the titillation of the people beyond the fourth wall (unless you’re doing some sort of erotic parody where that’s the point).