Questions & Answers about Minä luin haastattelun tänään.
Why does the verb lukea change so much to become luin?
This is because of consonant gradation and a vowel change! When you make a closed syllable by adding the -n for "I", the strong consonant k in lukea drops out entirely to make the weak stem lu-. Then, the stem's final -e drops away when the past tense -i- is added. Together, luke- + -i- + -n becomes luin.
If the 'k' drops out in luin, does it drop out for all the other past tense forms of lukea?
Only in the closed syllables! The k drops in forms like luin (I read) and luit (you read). But in the "he/she" form, the syllable is open, so the k stays strong: hän luki (he/she read).
Why does haastattelu have an -n at the end here?
It is the object of the sentence. Because you completed the action (you read the whole interview) and the sentence is a positive statement, the object takes the accusative case. For singular words like haastattelu, this looks exactly like the genitive case with an -n ending.
Could I drop the word Minä from this sentence?
Yes, absolutely. The -n ending on luin already tells us who is doing the action. You can simply say Luin haastattelun tänään. Including Minä just adds a bit of emphasis.