Does only one correct spelling and pronunciation exist for each English word?

Answer 1

No. There is are words that have different spellings in different countries, like in America and Britain. Colour in Britain and Color in America, for example. Some have two acceptable spellings, like spelt and spelled, relating to how you spell a word. In America, words tend to use a more phonetic spelling, so you have center and kilometer and traveling, whereas in Britain you would have centre and kilometre and travelling. Lots of words have the same spelling and different meanings and pronunciation, which you can take from the context. Like you cry a tear, but if you rip something you are making a tear. You can read a book, pronounced like reed, but once you have finished, you read the book, pronounced like red. There are many other examples of these kinds of things to show you that no is the answer to your question.

Answer 2

No, there can be variations in spelling and pronunciation for some English words depending on regional dialects or historical usage. However, there is usually a standard spelling and pronunciation accepted in formal contexts.