Do the data remain in the text fields of webforms if we navigate to another webform?

There is no direct way to retain values in webform but you can do it with the use of localstorage and jquery. You have to store values in localstorage before leave page and bind values again in respected fields in the document.ready function then clear localstorage.

No. Values retain via viewstate in webforms. Viewstate is page level. It could retain during postback.