Image Optimization, long list data fetched from Rest API and rendering the top of the home page on a new user’s first visit

Can someone help me to answer these questions? I did it but I would like to have an expert opinion on these field. Here we is the case:

Please provide options of what someone can do to improve the performance of a website for each of the following topics. Imagine that an engineering manager has given you the freedom to improve the following items on a website for the next month. What would you tell the manager you would take a look at? Bonus: Please add any details to your list, if time allows, to showcase your knowledge.

displaying images
displaying long lists of data fetched from a REST API
rendering the top of the home page on a new user’s first visit as soon as possible