"in-between" vs "in between" vs "inbetween" vs "between"

Question

When to use "between" and when to add an in and say "in between" has become clear from the two very related SE posts: "In between" or "between"? and 'in between' or 'between'. Apparently the in can always be omitted but is optional to add when "between" is used as a preposition for physical (and apparently also time-wise) comparisons:

There is a puddle [in] between us. ^{Optional "in"}

There is some tension between us. ^{Don't use "in"}

Question 1: Is this always correct? Are there never situations where the in is mandatory?

Question 1a: And equivalently, in order for me to understand the proper usage: what difference does the word in make in the sentence? Does it not make a difference? Can I safely omit the in completely in any context and never bother with this again?

When I do choose to use the in in relation to between there apparently are several options:

in-between

in between

inbetween

The two first-mentioned seem well-explained in Should I use "in between" or "inbetween" in the following sentence?: the "in-between" is an adverb. But an answer in that post indicates that the latter form "inbetween" with no dash or space does exist.

Question 2: What exactly is the difference and meaning of these three versions? And do they all exist?

Answer 1

Question 1. and 1.a) I doubt that the preposition in is ever required. It likely has to do with regional usage and style rather than correctness. E.g. British English vs. American english. See: https://www.quickanddirtytips.com/education/grammar/prepositions?page=1

Question 2.) According to this answer and Merrium Webster, In-between is an (adjectival) noun or idea. For example, one could say "We are in the in-between phase of this plan." "In between" can be thought of as an adverbial phrase as in, "The interviewer and interviewee were sandwiched in between two ferns."