Q: How can I programmatically create or add new Taxonomy Terms using PHP code?
A: Call the function taxonomy_save_term() passing in the details of the new taxonomy term.

Here is a link to a handy article that shows how to output a node's taxonomy terms (as links) from a drupal content template (contemplate).

http://drupal.org/node/92838#comment-190334

Q: How can I change the taxonomy term selection widget from the default list-box to checkboxes or radio buttons?
A: Just install the 'Taxonomy Super Select' module.