"I ran yesterday."
Yesterday is not the subject of the sentence, and so is not marked with が. Most relative time phrases are not marked with particles at all :)
Yes. Unless your sentence explicitly needs to draw attention to an action occurring yesterday. In English, feel the difference between "yesterday, I did the dishes" and "But I did the dishes yesterday"
Can somebody explain the relationship between ました here versus まして as in はじめまして?
ました turns the verb into its past tense. して is the imperative form of some verbs like はじぬます. はじめました: started はじめまして: let's start
Why wasn't "昨日私は走りました" accepted? Is it because of the "私は"? If so, where in the sentence should it go, if not in front of the time?
Why won't the kanji for "run" let you hear the pronounciation? In some exercises when you select a kanji it will do that, but all of them worked except run.