Is there a way to set a default schema for each user in MySQL and if so how? Where user x would default to schema y and user z would default to schema a.
There is no default database for user. There is default database for current session.
You can get it using DATABASE() function -
SELECT DATABASE();
And you can set it using USE statement -
USE database1;
You should set it manually - USE db_name
, or in the connection string.