Looks like the following station closure dates were:
-Paul Street: 2005
-Broadway (Burlingame): still open on weekends, but not on map due to no weekday service
Atherton: 2020
-Castro (Mountain View): 2000
Regarding the name change of the 4th St station, it looks like it may have happened in 1998 when the N-Judah was extended to 4th & King, so name of Caltrain station was changed to have same name as Muni station.
Comments
-Paul Street: 2005
-Broadway (Burlingame): still open on weekends, but not on map due to no weekday service
Atherton: 2020
-Castro (Mountain View): 2000
https://web.archive.org/web/20050526034241/http://www.caltrain.com/news_2005_5_23_broadway_and_atherton.html
https://www.sfgate.com/news/article/little-used-mountain-view-station-closing-2891405.php
Would love to see a source.