Why is my cat eating cardboard boxes? Should I be worried about it?

The first thing you need to do is have him examined by your vet to check for any underlying medical conditions (like a dental problem) before you just assume the problem is behavioral. He could have a bad tooth or even a malocclusion. I am suspicious of a dental issue because of the drooling you described. If no medical condition is found then I suggest you do some Feliway and some environmental enrichment as he could be stressed and/or bored. ( https://www.feliway.com/us/Products/FELIWAY-CLASSIC-Diffuser ) ( thedrakecenter.com/materials/environmental-enrichment-indoor-cats ) ( https://www.youtube.com/watch?v=AejmrLa_Cs4 )

That is a very common behavior in cats! If the papers are something you don't want them eating, keeping it out of reach or safely in a drawer is best. If they like chewing things, giving them their own box to chew on, or even toys such as a cardboard scratching post to play with can help divert their attention to those items instead.

Cats tend to enjoy chewing on things, such as plastics, boxes, etc. It would be best to keep Ella away from any plastic bits she may accidentally eat, and distract her with other toys and treats as needed. If she does eat some plastic, vet care is best.

This can be a sign of pica, and it is bad for Mochi to do. It can cause an obstruction. Pica is a symptom of an underlying disease such as FIV, hyperthyroidism, anemia, feline leukemia, dental disease, diabetes, and others. I'd have her seen by a vet for this behavior. I hope this helps!

Some cats chew on it because they like the taste and texture in their mouth. This can be a concern because if the cat eats it, it can cause a foreign body. When I was in college, I had a cat eat the plastic streamers from a pom pom, and she had to have emergency surgery. I would keep Sasha from doing this. I hope this helps!

No, not likely to be a dietary deficiency or due to a dental issue. It is probably boredom. I suggest you do some environmental enrichment for him. ( https://www.thedrakecenter.com/materials/environmental-enrichment-indoor-cats )

In all likelihood, Fern's fondness for paper is likely a normal play and exploration behavior. Young kittens are still learning about their surroundings and sometimes get into trouble in the process. Obviously, try to avoid letting her eat paper when possible, but a bit here and there is unlikely to cause any significant problems. If she is eating a commercially available balanced kitten food, a nutritional deficiency is highly unlikely as a possible cause. Try to confine her when you leave the house to avoid unsupervised access to paper products, but I would expect her to grow out of this behavior. If you haven't already done so, take a stool sample to her vet to assure that intestinal parasites are not present, as this can occasionally cause animals to eat abnormal things. I hope that all goes well!