Давайте разберем каждое предложение и заполним пропуски подходящими вспомогательными глаголами. Вспомогательные глаголы помогают образовать различные времена и формы глаголов.
    - 
        Have you seen my mobile? I've been looking for it for almost an hour.
    
- 
        Jane has finished tidying up her room, and now she is going out with her friends.
    
- 
        If brunch isn't eaten and no Instagram photos of the food were posted, did it really happen?
    
- 
        Do you know people who are always in some form of drama? Why does trouble always follow them?
    
- 
        Luckily, they were able to raise $30,000 to help those people who were affected by the earthquake.
    
- 
        According to popular theories, homework was invented by Roberto Nevilis in 1905 as a form of punishment for students in Italy.
    
- 
        People say that money is not the key to happiness, but I think if you have enough money, you can have a key made.
    
- 
        A study finds that the number of active daily Threads users in the UK has dropped from 8 million a year ago to only around 5.6 million now.
    
- 
        In Rome and Greece, trousers were associated with 'barbaric' cultures; civilized women and men wore tunics.
    
- 
        After any gathering where food is served, there are often plenty of leftovers for the hosts and guests to enjoy later.
    
- 
        Why do rich men use most of their money to get richer while poor men use most of their money to look richer?
    
- 
        Modern economics was born in 1776 with the publication of Adam Smith's book, "An Inquiry into the Nature and Causes of the Wealth of Nations".
    
- 
        Over the last 3 days, I have seen about a few people walking around in pyjamas. Are pyjamas the new style on the street?
    
- 
        Those who had high-quality sleep were more likely to be successful in their weight loss efforts than those who did not sleep enough.
    
- 
        In Ancient Egypt, furniture was primarily constructed using wood, but other materials were sometimes used as well.
    
Теперь давайте подытожим, как мы подошли к заполнению пропусков:
    - Мы определили, какое время и форма глагола нам нужны в каждом предложении.
- Мы выбрали подходящие вспомогательные глаголы в зависимости от контекста и времени.
- Мы проверили, чтобы вспомогательные глаголы соответствовали основному глаголу по времени и числу.
Если у вас есть вопросы по какому-либо из предложений или по использованию вспомогательных глаголов, не стесняйтесь спрашивать!