Are 先に and 最初に interchangeable? For example in these sentences are there any nuances?
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先に literally means earlier and 最初に first although both may be translated as first like the examples.
As for the examples, both mean the same because どっち usually assumes two things and what is put earlier is what is put first.
On the other hand, consider the following when there are three people A, B and C.
2 unambiguously means A was the first to come. 1 could mean A was the first or A came earlier (than someone the speaker has in mind implicitly).
Note that どれを先にいれるんですか and どれを最初にいれるんですか most probably mean the same even if there are more than two things. I suppose this is just because asking about the second (etc.) thing to put is unlikely.