Is it possible to import DBs information_schema, performance_schema and mysql from mysql-community-server-5.6.x to mariadb-server-5.5.x? Is it possible to import the following DBs from an existing mysql-community-server-5.6.x configuration to a fresh mariadb-server-5.5.x :

+--------------------+
| Database           |
+--------------------+
| information_schema |
| mysql              |
| performance_schema |
+--------------------+


I guess no here because the table structure of mysql.users should be different between mysqld and mariadb.
Maybe some of it.

information_schema is not a real set of tables; it is in-memory data that pretends to be tables.  So, a definite "no" for that.

performance_schema is mostly transient, so don't bother.

mysql changes between versions, so it would be risky to do so.  Use mysqldump (or other tool) to dump routines.  Do SHOW GRANTS ... to get grant statements to replay; this is somewhat tedious.  Start fresh for most things in mysql.

Also, Oracle 5.6 to MariaDB 5.5 is a step backward in many aspects.  Can't you go to 10.0, at least?  That version has more of what is in 5.6.