Does the <basefont> tag exist and what role does it perform?

No, the <basefont> tag is deprecated and no longer used in modern web standards (HTML5).

In earlier versions of HTML, it was used to set basic font parameters (size, color, type) for the entire document or a part of it if styles were not overridden.

Its role is now fully replaced by CSS styles.

Example of usage (deprecated):

<!-- Deprecated: Sets Arial font, size 4, and color #333 for the entire document -->
<basefont face="Arial" size="4" color="#333333">

Modern approach using CSS:

p {
  /* Applies Arial font, 16px size, and color #333 to all paragraphs */
  font-family: Arial, sans-serif;
  font-size: 16px;
  color: #333333;
}