TED DIBAR, (40s) swings his cape to the side, as he approaches Felix.
Do I need to continue to use the character's full name, or can I shorten it in subsequent mentions?
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All the screenplays I have seen always use the form of the name that the character is known by to the audience.
For example, if you tell the tale of Robert Williams, but all the other characters always address him as "Bob", you use "Bob" as the marker for this character. If, on the other hand, Mr. Williams is a teacher and only his wife calls him "Bob", while his students call him "Mr. Williams", use the form of the name that is used where the story happens: if it is a story about a teacher and told mostly in school, call him "Mr. Williams" in your script; if the story is about a husband who just happens to be a teacher but takes place mostly in private circumstances at home and with friends, call him "Bob".
Do not use abbreviations ("B."), unless the character is called "B." by his co-characters (e.g. "J.R." Ewing in Dallas).
If first names alone are confusing (maybe because the cast is so large or names are too similar), use the full name, even if the characters in the play/movie use the first name. But this should not happen, unless you need confusing names for plot reasons (e.g. a story about two women named "Joan").
Keep your script consistent. You do not want to confuse the readers. So, yes, always use the full name.
No, you do not have to keep calling the character by his or her full name. It would make it very awkward to have to read "Ted Dibar does this", "Ted Dibar does that", all the way through the script. Go ahead and call him Ted in the action lines. Or TED when it's formatted above dialogue.
And read scripts. They're all over the web (e.g., the mother-lode of tv pilot scripts here: https://sites.google.com/site/tvwriting/us-drama/pilot-scripts). You'll see how it's done.