I like that the long lines are displayed over more than one terminal line; I don’t like that vim inserts newlines into my actual text. Which part of .vimrc I should change?
I'm not sure I understand completely, but you might be looking for the 'formatoptions' configuration setting. Try something like :set formatoptions-=t. The t option will insert line breaks to make text wrap at the width set by textwidth. You can also put this command in your .vimrc, just remove the colon (:).