And they will be suing for what? For attempting to send more people to facebook? What's the damage?
Facebook has no right to have their arbitrary code on other people's websites. So they can't force any specific way to show their button. From the end user's perspective it's all the same.
Facebook could reasonably argue that by bypassing their established use policies for the like button, you are depriving them of value - in this case the value of the data that their JavaScript collects and sends back to them, and that you (the site owner) are being unjustly enriched through the use of their copyrighted image(s) on your site.
Except in cases of fair use, which isn’t nearly as broad as people think, the use of other parties’ images is subject to whatever licensing restrictions they choose to put on them. You can choose not to display their images if you do not accept those terms.
The reason sites want to have Like buttons is because they perceive value in that for the site. A C&D would be enough to bring anyone in to alignment that didn't have a wish for a very expensive day trip to court.
That’s a very broad question. For one thing, fair use is a concept only in US law. Other countries may have their own versions of it, but all of them have their own unique limits. Even under the US version, it is not at all clear that it would fall under fair use. If I start making t-shirts with the Facebook logo on them, is that fair use? No, it isn’t. Is there much difference between that and putting it on a website that I make money from? The right jury would say no.
Facebook has no right to have their arbitrary code on other people's websites. So they can't force any specific way to show their button. From the end user's perspective it's all the same.