When a tile says Player limit is 1
does that mean the same player can connect multiple times (getting pts each time)
is it referring to the number of connections in total the station can have
The player limit is the total number of different players that can connect to the tile.
So if a tile has a limit of 2, Red and Green can both have strings connected to it. Each of those players can have several strings on it. It might have 3 strings from each of Red and Green for a total of 6!
However, you only get points for connecting to a tile ONCE*.
*Except for the Marshalling Yard, which specifically gives you 1 VP each time you connect to it.