Why are log messages from imported module not shown?

I can't seem to raise the log level of a module's logger. I have a script which uses the root logger, and I want to only print its ERROR logs. However, the module I import, I would like to log granually on DEBUG.

In mymodule.py:

import logging
log = logging.getLogger(__name__)
log.setLevel(logging.ERROR)

def do_something():
    log.DEBUG("Module debug")
    log.INFO("Module info")
    log.WARNING("Module warning")
    log.ERROR("Module error")

and in myscript.py:

import mymodule
import logging

logging.getLogger().setLevel(logging.ERROR)

modulelogger = logging.getLogger("mymodule")
print(modulelogger)

modulelogger.setLevel(logging.DEBUG)
print(modulelogger)

mymodule.do_something()

log.DEBUG("Script debug")
log.INFO("Script info")
log.WARNING("Script warning")
log.ERROR("Script error")

Output when running myscript.py:

Module error
<Logger mymodule (ERROR)>
<Logger mymodule (DEBUG)>
Error:root: script error

1. Why am I seeing the level of the "mymodule" as WARNING initially? The module defines it as ERROR?
2. Why am I not seeing the INFO and DEBUG logs by the "mymodule" logger after setting its level to DEBUG?