Arduino Internet Connectivity and Control Question

I plan on making an automated pet feeding system, i would like to use a webcam that will allow the user to see the pet from a live internet feed from that camera. As well as allow the user to check on the status of the system from a webpage or a phone app, all over the internet remotely. i will also need to attach several other components to the project (Arduino microcontroller) as well, such as motors to deliver food, sensors to detect amount of food left, and perhaps even a pan and tilt module for the camera so it can move.

MY QUESTION IS: I'm not sure if the Arduino is Capable of this. I know the Arduino can control alot of components especially if i were to use the MEGA, but im more concerned with connecting it to the internet and controlling/monitoring the system remotely over a webpage?

Any help with this is GREATLY appreciated, and feel free to ask for more information if needed!