I've created a schema to handle some specific features.
In the schema there are a couple of tables used by many functions (more than 20).
In other words, I've created a schema as a package (as suggested in many points).
I wish, in a function of this schema, to be able to call each other functions of this schema without adding the schema name in the call instruction.
PostgreSQL isn't really designed for that - especially if you aren't formally creating an extension but simply putting stuff into a schema.
The script code you use to install your makeshift package should handle dynamic schema naming. It's a pain, do you really need to allow the name of the schema to be unknown at installation time?
You should read up on how extensions are implemented - you are basically writing your own CREATE EXTENSION implementation.
In any case, there really aren't any smarts here: explicitly schema qualify your function calls and forget that search_path even exists. Unless you are writing custom operators, and even then, consider search_path to be evil.