What is the meaning of the following sentence? You have successfully split a hair that did not need to be split. Source: this post on the Programmers Stack Exchange.
Does the "in" imply multiplication, in which case split in half is correct, or is it division? It sounds like the latter to me, but I've heard it used both ways.
2 You can do "a split" or "the splits". They are interchangeable. But you would never say "a front the splits". You would say "a front split" and walk away smiling, even if you pulled a groin muscle.
Split infinitives involve the to-infinitive specifically. The "to" not a "preposition"; it is a infinitive marker. Lastly, I found your arguments about "wanna" & "gonna" unconvincing and irrelevant because these words are informal and the argument about split infinitives is most certainly about prescriptivism.
The semantic trickiness here is that so many terms for something that is whole use un- or in- and a word meaning divided in order to convey what you mean. Unsplit, indivisible, uncleft, unsundered, uncut. Your other options are in the realm of monolithic, like integrated. So it's a good question, but I can't think of a better answer.
Every entry has a word split into syllables, and technically speaking, according to traditional rules of typesetting, you can hyphenate a word at any syllable boundary. For example in the Merriam-Webster's online dictionary, the entry for "dictionary" reads "dic·tio·nary"—so you could hyphenate anywhere there appears a centered dot.