Can gerbils chew on egg cartons, t-shirts, popsicle sticks, or newspaper?

It is best to give them things to chew on that are made for guinea pigs but if you are going to use boxes it is best for them to be plain with no writing/ink. Here are some good treats for them. ( https://www.petco.com/shop/en/petcostore/product/oxbow-timothy-club:--bungalow-medium ) ( https://www.petco.com/shop/en/petcostore/product/oxbow-timothy-club:--bungalow-medium )

I would not give Jelutong wood to a gerbil as it has gum that may be detrimental to your gerbil. Meranti has been reported to cause eye, throat, and skin irritation, so I am not sure if this would be a good idea for giving to a gerbil to chew. You may try giving him bamboo or coconut shell for a chew toy.

No. Hot glue is plastic nawed, so if your hamsters chews and ingests it, there is risk of obstruction. A PVA glue or any glue labeled as 'child safe' would be a better option. Cardboard tubes or rolls are safe and hamsters love shredding them or crawling through them. Popsicle sticks, when chewed, may expose a hamster to sharp splinters. For this reason they are not recommended.

It would depend on the species of vine being offered. Certain woods, such as Apple, Ash, Sycamore and Willow, are safe for gerbils to chew on. Gerbils like to burrow, so the layer of bedding should be 5-6 inches deep.

A toilet paper roll (without the toilet paper on it) is a fine toy for a chinchilla. Unless your chinchilla for some reason decided to eat it all in one sitting, it shouldn't be an issue. When I worked as a zookeeper we used to put treats inside a toilet paper roll and put hay or paper towels in each end so they had to work to find their treat!

Wow I can't believe she is allergic to plain care fresh paper bedding. You can always try plain AstroTurf or reptile carpet which is really easy to clean but may not be as comfortable. I honestly think your shredded t-shirts are a great idea as long as she isn't trying to eat any of it.

There are a variety of creative ideas for Rat toys/enrichment that can be made from many things that are commonly laying around the house. Below are a couple of links with some great ideas and information about rat enrichment. https://www.dapper.com.au/toys.htm http://www.afrma.org/enviroenrich.htm I hope that helps and all is well with Yuki.