stplush wrote:

I'm unsure of what お's purpose is here.

私の国について少しお話しましょう。

Plus I don't understand the last portion of this sentence.  Is 見当もつかない one word?

この仕事には何日必要か見当もつかないね。

Thank you.

o + noun/verbmadeintonoun + shimasu is a form of kenjougo, which is a part of keigo, that is, honorific speech. It's used when you're talking about someone of higher status and the verb is something you would do. So it's actually pronounced "o hanashi shimasu".

見当もつかない is not one word, no. It's kentou mo tsukanai, which is an ideomatic phrase meaning "having not the slightest idea".