I think that their original intent was convenience. They just wanted you to start in the area they made so that they wouldn't have to make another area. Of course now it's open to all sorts of story opportunities.

Where our guardian spawns outside the wall is where the first raid of destiny was supposed to be unlocked in "THE GATEWAY" but nobody ever opened rasputins warmind in order to execute "MIDNIGHT EXIGENT" No one ever figured out the doorway of the pocket infinity or the true purpose of the gjallarhorn that is connected to 3 anti matter death rays on earth with 2 open doors and 1 closed!

To be honest we're not told exactly why. Though we can assume some reasonable options. We know for example that during the Collapse countless humans fled Earth from bases such as the Cosmodrome. A human or Exo could have been in the process of trying to make it to a colony ship during the collapse and died. An Awoken guardian would have probably had to come later, following the collapse during the exodus back to earth.

The ghosts explored all over in search of guardians, not only on Earth but also Mars (where they didn't have any luck because of the Sand burying everything) and possibly other planets as well. Our guardian happens to have been found outside the Cosmodrone walls, presumably having died at some point after the collapse (as you can choose Awoken as your race it would have had to be after the collapse) but before the Fallen emerged, putting us most likely in the early dark ages. As to why we were in the Cosmodrone, no reason is given but given the timeline we would have died long before the Iron Lords existed or anybody had been risen by the traveller's light. It's possible given our surroundings that we were killed trying to make our way into the Cosmodrone, given the car pile up around us it seems that a lot of people at some point were trying to flee towards it, so it could have been a shelter of sorts. As to what we were fleeing from, I don't know. It wouldn't have been the collapse itself as they have to account for those who chose Awoken, so some time would have had to have passed for us to have made our way to earth after the collapse before whatever events lead to our death. I think this is one of the things that is purposely ambiguous so that you can make up your own backstory.

Well we were just a human or Exo during the collapse who died trying to get on the ships that were trying to escape the Darkness. Or in the case of the Awoken, an Awoken person who came back to Earth and managed to get sniped by a Vandal outside the wall.

This is something yet to be discovered. There are some speculation about the past of our guardian, but there is nothing in the Grimore about our true identity. Very likely, the location of our recovery was just randomly selected by Bungie to start the story mission. If there is something more, it could be reveal in the upcoming DLC