There must be 'subtle?) details missing as I cannot reproduce this here.
First of all, I cannot see the caret disappear. When there is no text on the line and no text selected, it is normal that it falls back to the default font, i.e. the font set via AdvRichEditor.Font.
When I delete text on the first line and reenter text, it uses the font of the text already there, so it moves back to Arial 10. I cannot see that it uses Tahoma after deleting the line?