She used to be a shy person, but nso she took speaking lessons. Now she is really poised to accept any invitation to speak at conferences.

To be poised to do something usually implies that a preceding action set you up to do the next thing. It is hard to explain, but it feels like a step is missing here. In the correction above, I added a phrase that I think makes it sound more natural (American English).

I was so blowled overn away by her new book that I plugged it in an article on Linkedin.

I personally haven't heard the phrase "bowled over", but I'm not saying it doesn't exist. Instead of "bowled over by", I would probably say "blown away by" in American English.

Also, when I first read this, I imagined you literally plugged a book into an electrical outlet (plugged it in) :). But with more context it would make sense. That's the right usage of plug, as in to promote something.

My grandfather really had the gift of the gab, but his daughter did not take after him and tries to avoid all social interactions.

I don't hear it very often, but I think the expression is "the gift of gab" in American English at least.
With just a comma, it's a run-on sentence. Adding "but" makes the two ideas flow more naturally.