It seems slightly odd, given that there are different traditions of between-sentence spacing, that there doesn't seem to be a Unicode character for the kind of space between sentences.
Not the person you asked, but I think so. Some fonts also convert “fi” into a character where the letter-spacing is very small and the i loses its point, so there’s definitely a mechanism for letter combination / adaptive spacing.
I thought the rule was that ligatures shouldn't cross syllable boundaries. Like the fi in "fine" can be replaced but not the fi in "barfing", so it would need to be a bit more than a lookup table. Or maybe a dictionary-sized lookup table isn't a problem anymore.
Are fonts Turing-complete now? I have a feeling they'll become such if not already there; a little programs, complete with configuration switches so that you can control if and how a combination of characters get converted into a ligature depending on surrounding context.
There are (maybe not explicitly designated as such, but en-space or em-space would be reasonable, I think). The problem is that there's no sane or consistent way to actually input these characters (besides perhaps a macro that detects double-spaces and replaces them with a single somewhat-longer-than-normal space).