Tato věta je z Destination C1/2 v unitu o modálech (str 71 úplně dole) http://www.tlu.ee/…20(7-12).pdf

Opravdu se to dnes tak používá? Jak ji nejlépe dát do češtiny? Chápu, že Alan na tom meetingu tedy nejspíš byl a dělal problémy? Nebo nebyl? já vlastně vůbec nevím.

Viz Konjunktiv v angličtině (the subjunctive mood) 

Děkuji, přiznám se, že mi to pomohlo jen částečně Pořád vlastně nevím jak vypadala ta situace v reálu . Je to tedy kombinace konjunktivu, modálu a perfektního infinitivu? Já myslela, že je to spíš minulý modál.

I can't find the sentence in the link you provided. The question “Was it necessary that Alan should have been invited to the meeting?” is technically correct, but unnecessarily clumsy, and I doubt that a native speaker would say or write it in normal present-day parlance. You might find this construction in biblical, legal or formal style.

• Musel být Alan pozván na schůzi?
• Bylo nutné, aby byl Alan pozván na schůzi?

The (unnecessary) “should” is a subjunctive, and the (unnecessary) “to have been invited” is a past passive infinitive. The use of “was” already tells us we're talking about a past-time situation, so the past infinitive is not necessary.

It's not advisable to use a that-clause after “necessary”, because it just complicates the choice of the following verb form.

The simplest and most elegant construction after “necessary” is necessary for someone to do something, necessary for something to be done.

Different ways of expressing the same question:

• Did Alan have to be invited to the meeting?
• Was it necessary for Alan to be invited to the meeting?
• Was it necessary to invite Alan to the meeting?
• Should Alan have been invited to the meeting?
• Was inviting Alan to the meeting necessary?

Out of context, we don't know if Alan was at the meeting or not.

Thank you! That puts my mind at ease

just to clarify, it's this tiny bit (the first link is a random link from google): https://ctrlv.link/Tx1B