Is there any way to access Google Inbox reminders via Gmail API or another way? I know that Google Inbox can show reminders from Google Keep, but can't find any information about how this communication is done.
You cannot get the reminders via the Gmail API at this time.
Google Keep, Now and Inbox have no APIs either sadly.
So if you are making an application, your cannot get the reminders of your users as of yet.
To get your own reminders though, simply type "What are my reminders?" into Google.