First: Using the SPLIT function, effects work on the upper part but not on the low part. I can't find how to make it work (or maybe it's not possible to use multiple effects?)

Hi g,
Welcome to YamahaSynth!

Here's what's happening... The CP4 Stage has 3 possible Parts: MAIN, LAYER and SPLIT, it has resources to apply Effects to any two Parts, simultaneously.

If you have a Main and Split, and find that you cannot activate the Effects for the Split, it's because they are currently active on the LAYER.
Navigate to the Layer Part and deactivate them.
They will now be available for the SPLIT PART.

Second: I recently installed ABLETON as i'm starting to produce. I would like to use the keyboard as a controller. Is there something i should do on the keyboard after connecting it with the USB cable, or I just have to setup from ableton?

See page 44 in the Owner's Manual for the basics of connecting your CP4 Stage to your computer.

The keyboard can send MIDI data to the computer.
If you want to record the CP4 Stage as audio, you will need an audio interface.

In general, the CP4 Stage can be used as a controller, typically you would turn the LOCAL SWITCH (also known as "Local Control") parameter to OFF.

The LOCAL SWITCH when set to ON lets the CP4 Stage's keyboard to trigger the CP4 Stage's own tone generator (local)
When set to OFF, the key presses only generate commands that go OUT via MIDI. This allows you trigger other synths, modules, soft synths, etc. without hearing the CP4 Stage also. If you want the CP4 Stage to sound, you can select it inside your DAW (ABLETON)

As instructed on page 44, you will need the Yamaha USB-MIDI driver to communicate with your computer type and operating system.
The driver will cause your computer to see the keyboard on USB Port 1.

Thanks a lot for the clear response!