They are not. Written Cantonese, in fact, uses the Mandarin grammar and the Mandarin lexicon and is, essentially, Mandarin, not Cantonese. There are substantial differences in the grammar and in the basic lexicon between the two to make them distinct languages. Written Cantonese that uses the Cantonese lexicon is incomprehensible to a Mandarin speaker, either, just as the spoken Cantonese is.
No they're not. Time to go studying linguistic before writing false statements on the internet. Even if most characters and words are shared in-between Sinitic languages, there are difference in lexicon, grammar, syntax and other subtle grammatical phenomena. Phonology is also distinct. It would be incredibly painful for someone the write its native language using an input method made for another language.
The confusing part for me as a Shanghainese speaker though is that we don't have a way to write Shanghainese, this "spelling" concept AFAIK simply doesn't exist. So I'm very curious to see who actually designed this functionality and what does it actually do.