I do not understand why I have to specify NumberStyles.Float when using decimal.Parse and not for double.Parse
I can do:
var tmp = double.Parse("1e-2");
but not:
var tmp1 = decimal.Parse("1e-2");
Because a System.FormatException (Input string was not in a correct format) is thrown
var tmp1 = decimal.Parse("1e-2", System.Globalization.NumberStyles.Float);
someone can tell me if there is a good reason behind this behavior

It's just behaving as documented. From Double.Parse:
The s parameter is interpreted using a combination of the NumberStyles.Float and NumberStyles.AllowThousands flags.
Note that NumberStyles.Float includes NumberStyles.AllowExponent.
From Decimal.Parse:
Parameter s is interpreted using the NumberStyles.Number style.
NumberStyles.Number does not include NumberStyles.AllowExponent.
I can't reproduce your bizarre stack traces which appear to show the same call failing just after it's worked:
Decimal.Parse("1e-2") always fails for meDecimal.Parse("1e-2", NumberStyles.Float) always works for meDouble.Parse("1e-2") always works for meDouble.Parse("1e-2", NumberStyles.Float) always works for meAs for why the "default" number style differs between the two - I suspect it's because double values typically are used in scientific scenarios where exponent-based representations are common, but decimal values typically aren't.
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