Regarding Frodo's age..
Frodo and Bilbo have the same birthday September 22nd. 33 is the 'age of adulthood" for Hobbits. When Bilbo was turning 111, Frodo was turning 33 HOWEVER Frodo had been living in Bag End since his 20s so he was kept looking youthful via the one ring even though by the time he leaves the Shire is is 50 (same age Frodo left the Shire).
If you look closely Samwise does appear more youthful at the birthday party.

Now,I hate when the screenwriters ADD scenes to a movie. The scene with Strider falling off the cliff did not need to be made up. With any book-to-movie there are always plenty of scenes that people loved in the book that could be included in the movie rather than making new stuff up. I think that it comes from people's tendency to want to 'improve' the book-to-movie. <ponders the Dune movies>

Even though we all love reading the books and visualizing the scenes for ourselves we love WHAT THE AUTHOR WROTE. We want to SEE what we've only been imagining for so long. It's kind of like having heard about a resteraunt only to get there and find that the resteraunt has been redecorated.