Just win some games of your choice to unlock these designs.

Aqua Design - Win 10 Card Games
Bamboo Design - Win Mahjong Solitaire 5 Times
Brick Design - Win 50 Card Games
Cloth Design - Win 5 Card Games
Digital Design - Win A Game 15 Times
Fall Design - Win Koi-Koi 10 Times
Marble Design - Win 30 Card Games
Mum Design - Win Mahjong Solitaire 10 Times
Paper Design - Win a game 10 Times
Plum Design - Win Mahjong Solitaire 15 Times
Space Design - Win 40 Card Games
Stone Design - Win a game 5 Times
Summer Design - Win Koi-Koi 5 Times
Winter Design - Win Koi-Koi 15 Times
Wood Design - Win 20 Card Games

Hard Mode - Beat Easy in Stamp
Normal Mode - Beat Easy in Stamp

You can use a special color in pictochat after you complete Stamp mode on Hard.

These Games will be available in Free Mode after you won them for the first time in Stamp Mode.

Field Tactics - Finish Level 3 in Stamp Mode

Ludo - Finish Level 2 in Stamp Mode

Shogi - Finish Level 4 in Stamp Mode

Word Balloon - Finish Level 1 in Stamp Mode

You can change the lounge music in the settings menu after accomplishing clearing mission mode.

When you chat to people online from your friend list you can see a grey button button that says STAMP. This button allows you to add stamps to your pictochat area in the form of different colors and shapes.