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Home Square - PlayStation All-Stars Battle Royale Kiosk
Play and win the Beat Down game to get the Sticker Album active item (25 slots) as well as individual stickers that show up on your reward list, but are not actual Home items. They can be viewed using the Sticker Album.
It's an easy game to win, just select the highest value characteristic and most of the time you'll win the card. Once you have all 20 cards the game ends. I only played once and it gave me five stickers. There may be some additional reward if you collect all twenty stickers.
UPDATE: After playing three more times I won all 20 stickers and it gave me the Beat Down game (25 slot active item). However, it does not appear to be a multiplayer game, and beating the AI is ridiculously easy, and it didnt give anynadditional rewards, so not sure why anyone would want this. YMMV
BTW: I played a fifth time in the public space and no additional rewards.
Home Square - Hed Kandi Music Unlimited Kiosk
Click X when it says "Want to Party with Hed Kandi" and use the kiosk to relocate to the Hed Kandi Event Space to receive Hed Kandi Headphones (locomotion item, not a wardrobe item) and Hed Kandi Hotpants (female only obviously).
Once there, go to the Music Unlimited Kiosk and click X, and then click on Play. Do not exit until the reward message alert pops up. You'll get a complete Hed Kandi outfit (has special dance animations when standing still - like the Ford Snych outfits) as well as two active items: Hed Kandi Outdoor Fireworks and Indoor Fireworks.
The headphones locomotion item when activated will make your avatar (when standing still) do a dance move similar to the one the Hed Kandi outfit does.
The fireworks look nice, but... The indoor one takes up a whopping 32 slots, and the outdoor one takes up 35 slots! Also, the display only lasts a few seconds and doesn't repeat, so you have to keep clicking play each time.