Whether you use Shelly WLAN light bulbs, Philips Hue or even smart light bulbs from different brands: The Shelly Plus i4 DC is compatible and can control them all.

No
That is not possible

** Disclaimer: I don't know Hue well, have always avoided it as expensive and lock-in.
Not directly without further effort. To my knowledge Philipps Hue is based on the Zigbee network protocol while Shelly WD speaks Wifi. This means it needs a device that "speaks" Zigbee and Wifi - there are many possibilities, for example based on Home Assistantc (HA). HA is open source and can be operated on DIY or commercial hardware.
Another variant is probably MQTT, although I have had mixed experiences with this myself.

Shelly has just released an update to their firmware in beta mode (so not yet officially deployed) which should, if I understand correctly, be able to handle other integrated buttons/actions. See their Facebook page for more details.