To get a Shiny Rotom, you would have to be pretty lucky. However, there are ways of boosting your Shiny chances like with the Masuda Method, which is where you breed 2 Pokemon from different countries (for example a Japanese Ditto and an English Rotom). The resulting Rotom in the egg then has a slightly higher chance of being Shiny.
To change its form, go to the Pokemon Lab and on the second floor there are some boxes in the bottom right of the room. Talk to them and you will be able to change its form.