Yes. With your Explore, you need to stick with the really thin inexpensive felt. This is generally the type you find at most craft stores. With your Maker, you can cut thicker wool felt such as our favorite from Benzie Design: https://www.benziedesign.com/ Our tips for cutting felt with your Explore: https://makersgonnalearn.com/videos/how-to-cut-felt-with-the-cricut-explore-air/ and our tips for cutting felt with your Maker: https://makersgonnalearn.com/videos/how-to-not-fail-cutting-felt-with-your-cricut-maker-fun-felt-banner/
No, you cannot cut MDF with your Cricut machine.
With your Cricut Maker, you will want to use the Knife Blade. We have more information about the Knife Blade here: https://makersgonnalearn.com/cricut-knife-blade-for-beginners/
With a Cricut Explore or Maker, you can use a Cricut Scoring Stylus. There are also Cricut Scoring Wheels (single scoring or double scoring) available for use with the Cricut Maker only. We generally prefer to use the Scoring Stylus no matter which machine we are using. You can find more information about these tools here: https://makersgonnalearn.com/cricut-blades-and-tools-explained/
It depends on the thickness of the leather. With the Cricut faux leather, you can use your fine point blade since it is so thin. The Cricut Maker can cut genuine leather up to 7 oz. thick with the Knife Blade. If using real leather up to 3 oz. thick, you can use your Deep Cut Blade instead.
The Cricut Explore can cut craft foam, foil acetate, plastic grocery bags, mylar, stencil film, and transparency. The Cricut Maker can cut everything the Explore can as well as plastic canvas and plastic packaging.
Yes, it can cut some wood products, but we highly recommend you stick to Cricut brand wood products. With a Cricut Maker, you can cut Balsawood that is 1/16″ or 3/32″, Basswood that is 1/16″ or 1/32″, and Wood Veneer. The Cricut Explore Air 2 can cut Wood Veneer.