Mark Cirino∗ notes this as an instance of Hemingway’s use of literally translated Italian idiom to signal that a conversation is being carried on in Italian.
In A Farewell to Arms, Hemingway needed to balance contradictory challenges, representing members of the Italian Army speaking to each other as authentically as possible—in Italian—while still allowing the novel to be understood by an English-speaking readership. His main strategy in overcoming these obstacles was to produce literal translations of common Italian phrases and words. (Cirino 46)
Italian pescecani (literally ‘fishdogs’) is composed of the same semantic elements as English dogfish, and has the meaning “shark”; but it is also a slang term meaning “profiteer”, exactly as oerkelens surmised.
∗ ‘“You Don't Know the Italian Language Well Enough:”The Bilingual Dialogue of A Farewell To Arms’,The Hemingway Review, 25.1 (2005),43-62
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.
Best Answer
This is not a real word. At least it's not in any dictionary I checked. Either Milne made it up, or he used a word which his real son Christopher made up. The closest real word I can find is 'whiffle', which is a noun ('a soft sound, like that of breathing or a gentle wind') and a verb ('make a soft sound, like that of breathing or a gentle wind'). I can't find the adjective 'whiffly', but it would make sense. A child mishearing or playing with language could easily change 'whiffly' to 'whoffly'. (In general 'o' sounds louder and deeper than 'i' - think of ping pong or ding dong.)