Sockets in Europe
Type CType EType F
Your the US plugs don't fit the sockets used in Europe.
Travelling from the US to Europe means two changes: plug and voltage. Almost all of continental Europe uses round-pin Type C/E/F sockets (the UK and Ireland are the exception, with Type G), so your flat US plug won't fit, and Europe runs on 230V against the US 120V.
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Yes, for the plug shape. Your dual-voltage chargers handle the 230V automatically.
A Type C adapter covers the continent; the UK and Ireland need a separate Type G adapter.
Dual-voltage gear yes; single-voltage 120V appliances risk damage on 230V.