I accidentally deleted my original reply, sorry. I'm reposting in light of your edit:
We use accusative after В when it involves motion to or from. I don't know that that rule applies to other prepositions. Prepositional case when В involves location.
Check out the list of prepositions and associated cases I've posted above. It combines two charts from two different language sites.
As far as I know, the Russian word "к" is closest to the English word "to" in this case, but here Russian uses "в" (which actually is more like the English "in") because it is assumed that you are going to the school with the intention of going inside. With this in mind, would it be possible to say "Я иду к школу" to mean that I am going to the school building but very specifically not going inside it?
The Russian "в" + Accusative (4th case) would be translated with "to" as in direction. Я иду в школу = I am going to school (but I am not there yet) The Russian "в" + Locative (6th case) would be translated with "in/at" as in being at that location. I am learning Russian at university and I never used "Я иду к школу".
Just wanted to clarify, there is no Locative case in Russian. What you are calling the Locative case is the Prepositional case. - https://en.wikipedia.org/wiki/Locative_case#Russian
It depends on what discussion you read. As I understand it, "locative" is the name of the case now usually called "prepositional". It was called "locative" because it mostly had to do with locations.
Here is a quote from а University of Chicogo page:
"LOCATIVE: A PLACE is a setting, locating an item in space, time, or a metaphorical domain.
The locative is the only case in Russian that always requires a preposition, and is therefore often called the “prepositional case”.
Five prepositions are associated with LOCATIVE: A PLACE: в ‘in’, на ‘on’, при… ‘at’, о ‘about’, and по ‘upon, after’. The uses of о, на, and при are based upon human experience of physical location in the domain of our three-dimensional environment.
The domain of the preposition о is topics of thought or discourse, things that we think, talk, and write about. The use of the preposition по with the locative is relatively rare."
Actually both в and на are also used with the accusative case for locative related meanings , e.g, into, on to
It is mostly a situation whether you decide to use the traditional academic terminology, locative which is derived from the study of latin. Alternatively, you can use the more descriptive prepositional because in Russian, the locative always requires a preposition.
Basically, it is a question of how stuffy your professor is/was.
I believe that иду is associated with movement on foot.
English speakers want to invest the concept with a direction and therefore like to use going as a translation and look for a comparable word for coming.
My limited understanding of it is motion and that direction relative to anything or anyone is not included in the word and the motion is accomplished by the most basic means there is. Nor does it say anything about style, speed etc. It does not itself distinguish between walking, running, marching, crawling. Just your basic movement which, unless indicated otherwise, is assumed to be on foot.
Of course if you add a destination, then the direction becomes apparent. But the word itself does not convey direction of any kind.
Please correct me if I misunderstand the usage.
I believe it sounds like that because in normal speech people tend to fuse words together. It sounds like 'ye' because its saying 'я' and the 'и' from 'иду' together. We do it in english as well without even realising. If I listen carefully I can actually hear the full 'я' it's just that it starts saying 'иду' rather quickly.