It’s possible. We traveled from Fullerton to Santa Barbara in one day, but there was a delay at the LA station because the train had to back into the station as there is no through track. You would avoid this delay if you were traveling from Los Angeles.

You will have to call Amtrak with that question. On another note “Due to repairs on an unstable cliff in San Clemente that caused the tracks to shift, Metrolink and Amtrak shut down service and hope to resume it by Oct. 4, 2020.”

You can still do it.
There’s no assigned seating on trains so most likely if you have a group that large it would fill a train car.

There used to be a company that hooked on a Parlor car to Amtrak trains. But it seems they no longer operate due to the current public health issue (Covid).

My recommendation would be to go north to San Luis Obispo. The ride is a lot more scenic, and downtown SLO is within walking distance. If you are set on going south downtown Los Angele (Union Station). From there you can walk to Olvera Street and Chinatown. There are homeless people in and around the LA station. something to keep in mind. One-way travel time to both destinations is 2.5 to 3 hours.