What are the font sizes we should consider in responsive Mobile and Web application?

Use a text input font size of at least 16px. If your text inputs have a smaller font size than that, iOS browsers will zoom in on the left side of the text input, often obscuring the right side and forcing the user to manually zoom out after using the text box.
secondary text : 13px or 14px

There are two types in web :
Text-heavy pages
Interaction-heavy pages

1.Text-heavy pages: Articles, blogs, news, etc. These are pages where the primary purpose the user has on the page is to read. There is very little in terms of interaction – perhaps just clicking a few links.

16px – absolute minimum for text-heavy pages
18px – a better font size to start with. You’re not printing out a single-spaced Word document; you’re writing for people sitting a couple feet from their decade-old monitors.
20px+ – may feel awkwardly large at first, but is always worth trying out in your design app. The best-looking text-heavy site on the web, Medium.com, has a default article text size of 21px.
2.Interaction-heavy pages: Apps that involve more hovering, clicking, searching for an item in a list or table, editing, typing, etc. There may be plenty of text on the page, but it’s not stuff you read straight through like a book.

Example: Google Calendar 2019

  • Month(Oct 2018): Regular 20px
  • Date (15, 16, 17 ...): Regular 48px
  • Event Name: Medium 12px
  • Event time: Regular 12px
  • Calendar("Other Calendars"): Regular 14px