Calendar app on the phone's primary job is to show you future events and alerts you. Past events don't need any alerts and doing nothing but take up valuable storage space on your phone. Hence, Calendar apps always have cut off date of storing past events. In the past, I remember my Windows Mobile phones only store past 2 weeks of the events. Google has been generous to store one year worth of past events.
Unfortunately, I don't see a search button on the Google Calendar app. So, to search for past events, you will have to go to calendar.google.com web site to search for all the old events.
Same goes for Gmail. It will store/sync certain number of days of emails on the phone (the default is 30 days but configurable). And there is a search functionality in Gmail app that can search through all your past emails even if it is not on your phone.