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.

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.

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.