American and British English use formality in this fashion as well. The usage is in line with the definitions presented here, as - even in your Tarun / Tina example - a formality remains an imperative (a must-do). But, as with all must statements (except maybe logical entailment), there are implicit conditions and consequences: you must do this [if you don't want that].
If something is a formality, you must do it if you want to remain within the bounds of normal, accepted or polite societal laws, etiquette or customs. If you don't care about violating the rules or the attendant repercussions, then you've no need to mind formalities. Logically speaking, obeying a formality is always optional. But, sometimes the situation or consequences make it obvious that there's only one reasonable choice to make.
In your example, Tarun invites Tina to the wedding for formality's sake, even though he doesn't want her to come. He's obligated to do so because he does not want to be rude, disappoint his family, or for some other similar reason. The language of his invitation makes it clear that he doesn't want her to go, but because he did extend some sort of invitation, he's obeyed the letter of the [social] law, and if Tina complains, he can say that he did invite her. We might say he extended her the courtesy of an (admittedly false) invitation.
Here's another example. Consider the CEO of a company interviewing a promising candidate for a job. The hiring process is lengthy, involving multiple screenings and a fair amount of tax paperwork for the government. The CEO is blown away by the applicant and says:
You're hired! Don't worry about the final interview or filling out these forms, those are just formalities at this point.
This means that the applicant will be hired, and the last interview is now just a hollow observance necessary for adherence to company policy. Similarly for the forms, filling them out is needed to legally and officially begin the employment, but the CEO is saying you work here now to the interviewee. These things are formalities - they're obligatory for remaining in compliance with governing rules - but the results aren't in question (they normally would be) and if the consequences of breaking the rules weren't important, the formalities wouldn't be observed.
Premise: a condition on which a logical argument is based.
Hypothesis: a plausible conjecture or explanation which can be proved or disproved by experimentation.
Supposition: a belief or notion that might be true or accurate, but might not. It can turn out to be false or inaccurate.
Best Answer
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."