The pearl strand - maybe (though that doesn’t necessarily mean the “pearls” are real). The case gives me pause, I think there’s a possibility that it’s reproduction vintage.
The steampunk style earrings are certainly fairly new, and cute!
I owned a pair of those steampunk style earrings-probably from the same manufacturer- in the mid 90’s. They were costume, certainly under $25. Fun to wear!
The pearls might be costume jewellery. If you rub a pearl against a tooth if it feels smooth it’s costume, if it feels “gritty” then it’s a real pearl (most likely cultured).
You can use a damp cloth (just water) to gently clean the pearls from any dust or grime.
The earrings are modern, as previously said, in the SteamPunk style, the metals will be brass / base metal.