1. Explaining these pronunciations involves two steps: first, figure out what the relevant environments are; and second, try to work out why the learner is producing these pronunciations in those environments. In terms of environments, [d] appears word-initially and word-finally, and [d] medially, between vowels; [ʃ] appears before or after an [Ι] vowel, and [s] next to other vowels. Since we know the speaker in this case is a learner of English, our first attempt at explanation might involve the patterns of her native language: we can hypothesise that in that language, [d] and [d] are allophones of a single phoneme, and likewise [ʃ] and [s] are allophones of a single phoneme, with a distribution like the one our learner imposes on English.
Predicted pronunciations would be: Daddy [dæði]; either [ð]; loathe [d]; ship [ʃ]; pass [s]; dish [ʃ]; usher [s].
2. One list of minimal pairs for initial position would be my – nigh – pie – buy – tie – die – guy – lie – rye. You can add me – key in a slightly different context. You should be able to produce similar lists medially and finally; what you won't find are cases of initial [ŋ], final [h], or for some speakers at least, final [r].
3. The main point here is that some pairs of sounds are in complementary distribution in this language: notably, voiced and voiceless pairs of sounds ([g] – [k], [b] – [p], [z] – [s]) do not contrast, since the voiced one appears initially and medially, and the voiceless one finally. Linguist A has noticed this, and uses a single symbol for each pair; Linguist B uses different graphs. Linguist A also uses a single symbol for [ŋ], which is a single consonant in this language, and represents [h] with each time it is pronounced. Linguist B uses for [ŋ], making it look like two consonants, and has no symbol for [h] word-finally. In short, A is using a system designed for this particular language; B is following English patterns, and is probably a native speaker of English.