This is a solution for people having this problem, I wanted to share this and calm people down.
A week ago out of nowhere I was unable to get online in Pokémon Y and I was always offline on my friend list, even though I had internet, I could browse the web and get on the eShop but got the error code 001 0502 whenever I tried to get online in Pokémon Y or whenever I went to my friend list ((The only things I did that day was play Pokémon Y offline and a few DS games in which I closed my 3DS) I thought this info might be useful if its somehow linked to the error). I browsed the web (sorry no source) and apparently this is caused due to a Spotpass error and it could last from a few days, to weeks, to even a month. Apparently Spotpass has an error in which whenever it tries to tag someone nearby it doesn’t, and for some reason this affects your friend list and your ability to go online in games. The solution was to wait a few days (A whole week for me) until the person who you tagged into your Spotpass arrives. Today I only met one person through Spotpass, but another person was already on my collection out of nowhere whom I've not seen before, in which I apparently met A WEEK AGO but I never saw him. After this event, I went home and tried to get online. I was online on my friend list and I could get online in Pokémon Y. I hope this information is useful and I hope Nintendo patches this bug. To all with this problem, hang in there!