1st question is, is it possible to change the appearance of your character? 2nd question, is it possible to transfer your character from one device to another device?
Please note that the social category is not for games developed or published by Chucklefish. Moved to Stardew Valley general.
yes, when you have max hearts with the Wizard (very easy to do if you present him with void essence) you will have access to his basement and magical mirror that enables change your appearance; by one device to another I think that you're referring to another platform, then the answer is no.
It is also possible to "change" your appearance by making new clothes at Emily's sewing machine with cloth and the various items required for each crafted clothing. Further permanent facial/body changing as stated above would be found after max hearts with the Wizard.
As william said, The Shrine of Illusions in the wizard's basement (accessible if you befriend the wizard) can be used to change the appearance options you chose at character creation. In the latest version of the game, you can equip new clothes. Befriending Emily will give you access to her sewing room, where you can make new clothes. Here is a link to the wiki: https://stardewvalleywiki.com/Tailoring The Shrine of Illusions only needs 4 hearts though.