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Yes, 'conversational' means casual and informal. Colloquial words and expressions are informal too. You may have noticed the difference between formal style and conversational style. 

You may sound informal as if you're just having a conversation or casual talk with someone. You're trying to convey your thoughts or opinion in an easy, conversational way, which may sound more natural and can be more persuasive or effective. 

Yes, too informal or casual isn't a good idea. For example, if you use such informal abbreviations as 'cuz', 'g2g', 'thx', you're driving them up the wall. On the other hand, too formal isn't a good idea, either, even though you're trying to write a business letter. You just need to sound natural and respectful. 

What really matters is that you should sound natural. How about these two sentences?  'What I'm trying to say is...' and 'What I am trying to say is...'. 'I'm' sounds just as good as 'I am', if not more natural. But, 'i am...' is too informal since 'I' (the first personal pronoun) is always capitalized in written English. 

So, it can be such a good idea to write in conversational, colloquial or casual, informal style, as long as you're not writing in a way that's too informal. 

Note:

'Conversational style' doesn't mean you're writing a conversation, though:

'What do you think of this?'

'I think Expector's really got a point there.'