"best way"?
If you have received a CSV file, "best way" IMHO is to use LOAD DATA command to have your MySQL db read the file and input the records into tables in your db. The MySQL manual shoud be able to give you full syntax for its usage. Be aware that you may have to play with the syntax for a few times before you have it working correctly. I'm telling you this beforehand so you can do all of yor practice on a development server before you duplicate the effort on your production server.
As far as your second question, try using
-h and -p in your MySQL connection parameters when you are attempting to connect to their MySQL server.
-h will allow you to specify the IP address of rington company's MySQL server.
-p will allow you to specify the port number of their MySQL server in case they are not using the default port of 3306.
Again, the MySQL manual will do a better of providing info than I can.