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for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.
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Accepted
Ramification divisor with base change
So the answer is:
Question 1 is wrong in general as R. van Dobben de Bruyn pointed out in the comment that the base change may not be normal.
So there is no conflict in Main Question 3.
See also the …
2
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Ramification divisor with base change
Let's work over $\mathbb{C}$. Consider the following commutative diagram
\begin{array}{llllllllllll}
E_1& \xrightarrow{f} &E_2\\
\downarrow{\pi} &&\downarrow{\pi}\\
P_1 & \xrightarrow{g} &P_2
\end{ar …