Hi I am wondering if the pet has to be fed in order for it to give it's effect like skill exp or life exp.
Looting and "Active" skills need your pet to be fed. An active skill would be "Finding resources" for cats. Passive skills +5% combat skill or +5% Life skills (or fishing, processing, karma return etc) are on all the time.
Hello there @MinhVu, I can see that you are wondering about Pet hunger. When a pet's hunger bar is empty, they will no longer loot items for you or use their special skills but you will still receive the passive bonuses like Talents and skills. I hope this clears things up for you. If you need any other help, don't be afraid to ask.
So is the fishing speed increase from Polar bear/Penguin active while they are hungry? Not sure if it is active or passive?