there is nothing specific you need in Amity square. It is just there as something to do besides battle
in hearthome city above the the contest hall
no pichu cannot go in amity square but pikachu can so :p i reckon pichu is cute though
corrn berry, magost berry, nomel berry, rabuta berry, belue berry, durin berry, pamtre berry, spelon berry, and watmel berry but they are very rare