What is the purpose of the קערה at the Seder? What difference does it make how everything is placed?
The Keara or Seder Plate is in fact not mentioned in the Mishna or Talmud. The first source for this custom is found in the Rishonim, see Tosfos Pesachim 101b sv lamah.
There are various customs how to arrange the seder plate each with it’s unique reason
The Maharil quoted in the Rama 473:4 opines that one should set up the plate so that the order things will be used should be accessible in that order. This is because of the rule of “ain maavirin al hamitzvos” not to pass over mitzvos.
Many follow the order of the Arizal. While there are kabbalistic reasons for his order, a rational explanation has been offered as well. The Shankbone and Egg commemorate the Korban Pesach and Korban Chagiga. As the 2 main mitzvos of the Seder night they are placed on top. The maror is eaten with the korban pesach and therefore placed beneath it. The charoses is eaten with the maror and so placed beneath it. The karpas is also connected to the maror, as it’s bracha covers the maror and so is placed along side the charoses. The chazeres is used only for the korech and so is placed at the bottom. Various reasons are given as to how we deal with passing over mitzvos according to this opinion, see Chok Yaakov 473:16.