Yes, you can. I think the link below will be especially helpful to you in the procedure as well as displaying available products towards achieving that end.
Hobby Lobby sells craft styrofoam sheets that are colorful and would be great for your kids to do crafts with. Craft Supplies for less also have many selections available of colorful craft styrofoam sheets. They have almost every color you can think of and they also have stick back styrofoam sheets available.
Yes there are many different types of laminating machines available. The one you purchase will depend on how frequently your going to use it, if it will belong to multiple people, and your budget.
yes there is such thing, check at your local craft store.
There are sheets you can buy at craft stores, where you can cut them into the shape you desire. Or you can print the desired shapes on to the sheets using your printer.
-I use a razor blade or the edge of a craft knife blade, VERY carefully.
Try searching your local craft store (e.g. Michael's). They usually have good prices on the sheets of cardboard and also have decorating supplies if needed.
Styrofoam sheets can be bought in any good craft shops. Some towns do not have those unfortunately in which case it is worth trying hardware stores or even looking online at what can be bought on Amazon.
There are many crafts one can do with sheets of plastic. Jewelry crafts, scrap-booking crafts, faux stained glass crafts and more. You can purchase sheets of plastic at any craft store and online at places such as eBay and Amazon.
There are several places one can purchase laminated plastic sheets. One can try looking at a store that sells arts and craft such as Michael's. One can also buy them online from Amazon.
You can buy leather sheets at craft stores, leather supply shops, online marketplaces like Etsy and Amazon, or directly from leather manufacturers. Make sure to check the quality and type of leather before making a purchase.
http://www.mcmaster.com/#hook-and-loop-rolls/=dwekf
You can get sheets of cork at craft stores. You can attach it directly to your wall, if you're allowed to. Or you can put magnets on the back and attach it to a fridge or other metal item.