This topic is covered at this link: http://grammarist.com/usage/distrust-mistrust/ For questions about synonyms, I suggest using a search engine such as Google.

I think that it's probably safe to say that there is - to all intents and purposes - no significant difference in meaning between the two words. The difference is so subtle that it's barely worth worrying about. Native speakers use them interchangeably. 'suspect' means something else entirely - you can check this in a learner's dictionary.

There is very little difference between these two words, but distrust is more common and perhaps slightly stronger. If you are sure that someone is acting dishonestly or cannot be relied on, you are more likely to say that you distrust them. If you are expressing doubts and suspicions, on the other hand, you would probably use mistrust.