I have a Macbook Air late 2015. I have just bought an Apple USB-C Digital AV Multiport Adapter. My Macbook Air doesn't charge nor pass through to the HDMI port. Is this device compatible ? I sent the first one back. I have done an SMC reset.

That adapter is meant to be connected to a 2016+ USB-C Mac to provide video output to an external display and supply power to the USB-C laptop.

A 2015 MBAir uses a Magsafe charger to supply power to the laptop. If you want to use an external display with your MBAir 2015 laptop, then you will need one of Apple's Thunderbolt 2 to video adapters (they have them for VGA and DVI, and possibly HDMI as well). To charge your 2015 MBAir you will need to use an Apple Magsafe 2 Charger.

Apple doesn't appear to have the Apple adapter available, but here is a third party Belkin HDMI adapter option:

Belkin 4K Mini DisplayPort to HDMI Adapter - Apple

Here is an Apple charger that is compatible with your MBAir 2015:

Apple 85W MagSafe 2 Power Adapter - Apple

This assumes you have provided the correct exact model for your MBAir. You can get the exact model of your Mac by clicking the Apple menu and selecting "About This Mac".

There are many such devices out there that are not compatible. The device's maker should be able to tell you if it is or not.