Yoast is always telling me to remove stop words, so I do. There must be a reason why they recommend it.

Stop word we shouldn't use in title never because google ignore it. and', 'in', 'of' etc..so please use always catchy title.

In title u have limited no. of characters to be displayed, so try to utilize it as much as by using the targeted keywords. Do not waste a single space using such stop words. It is not necessary to have a proper grammar sentence in title.It should make sense and reflect the theme your website offers.

Yes, but it really depends on if you are optimizing your title's for the SERPS, or for click throughs. You might have a very well optimized Title which gets you to the #1 position in Google, but the guy at #3 might have something that reads so well that it gives him a better click through than you, even though theoretically you should be getting way more traffic...

So it depends what you're trying to achieve. Personally I'd try please the SE's first, and then optimize for click through's later.

Yes, google don't count those stop words in the SEO factor. So you can just use WP SEOpressor or Easy WP SEO to take those stop words off.

I don;t think these are important. Google won't give much preference to them. It is important to have a proper title tag. Stop words can change your title tag.

Google doesn't consider stop words like "and", "in" , "of" etc. in their search results. Use your targeted keywords in title while making title tag.