I've heard anecdotally from a ton of players that are having these same problems.
1. Can't access in-game store.
When trying to access the store via the main menu in the game it brings you to an empty storefront. The only way to get DLC for the game is by using the web interface and downloading on PS3 later.
2. Can't download the 1.02 update released yesterday
I've heard some people have gotten this update. I've tried a few things but everytime I check for updates my PS3 says the title is up-to-date. I haven't been able to play vs. anybody on the new patch, which includes all PS4 owners. This is very frustrating as Guilty Gear is primarily a multiplayer game.
Thanks for any help.