AIs can query the web and parse the results, so it is possible for Claude to understand the question, search the web for movie schedule of a cinema, parse the website and give an accurate answer. It's also very possible for it to do it incorrectly or just pretend that it did that and give you a random time instead so that you are happy.

I can't imagine trusting an AI with something like this, where it's so easy to just check it yourself

I recently saw some fireworks on the beach and asked if there was something just to see what happened. It found the event in the internet and told as a possibly.

Nah they can get context and summarize web pages as they presently are. Not all do, and I'm not up to date on what ones do, but the expectation was Claude would find their schedule on their website online, would summarize it, and use that summary to answer the question and any followup ones that would've occurred.

Yeah, anything not taken into training yet will not be available for the bot.