As for the why, in Spanish questions are mostly phrased the same way as answers.

Basically I could make the statement that you are going to the shops by saying "you go to the shops" or I could ask you, are you going to the shops as "you go to the shops?".

This isn't a problem with spoken interactions because the context and tone of voice makes it obvious what is and isn't a question.

So the initial ¿ was added in the mid-18th century to make it easier to identify questions in written texts. It is a Spanish invention and not present in other Latin languages since it was invented by the official body that organizes Spanish (or at least "Spain Spanish"). It is also imported into other languages such as Catalan which were under Spanish domination, but it is more optional in Catalan. You only have to use it in Catalan if the phrase is ambiguous.

This punctuation mark is used a bit differently since it can occur with a phrase. So I can ask say, "you are going to the shops and ¿will you buy milk?". The ¿ there indicates where the question begins.

For similar reasons the ¡ was added to make it clear where an exclamation begins. "You went to the shops and ¡you didn't buy milk!"

Nowadays the starting ¿ is almost always dropped in informal writing but it's still the rule and whenever you read something written professionally it will be used.

Edit: the ¿ is no longer recommended for use at all in Catalan.

I can't answer your first question (but I'm curious about the answer - honestly I think it's an absolutely brilliant convention to let you know you're going into a question right at the beginning). However, I do know a bit about Greek paleography.

Ancient Greek did not start with any form of punctuation. The oldest Greek inscriptions and papyri AREWRITTENLIKETHISNOSPACESNOLOWERCASEAND no help figuring out what is going on. Alexandrian scholars started adding accents (mostly to differentiate words that would otherwise be completely ambiguous). Eventually they start adding a few punctuation marks like the interpunct ( · ) particularly in drama where the mark indicated a change in speaker. Eventually the system develops more complexity until you end up with a system with accents, breathing, the interpunct (which is essentially equivalent to an english semicolon), the period, and - to finally get to your question - the semicolon (;) which is the Greek question mark and remains in modern editions of Greek texts as the question mark to the consternation of generations of students.