Thanks fo the respons @jnashhawkins. The thing is, quite a lot of changes have already been made to the child theme. So rewriting it owuld take a lot of effort.
What wonders me is that whatever changes I make – they appear in theme editor and in the functions.php – nothing gets propagated and some old version is being served.
For example <p> tags with text I can find nowhere else in the theme.
Another thing is, whenewer I try to make a change in the theme editor, the update button keeps loading anf then suggests that the changes might not have been saved.
However, when I close the page and come back, the changes are there in the editor. Not propagated on the front-end though.
Is there some internal cache file or somethin that wordpress uses internally? Other than the theme files?