I see the pictures on your link, Jantan. This is not a Suzuki or a Yamaha. It is an inexpensive Asian melodica, probably made in China. It is not worth the cost or effort to try to replace the reeds or build a new casing. If you don’t like the tone and don’t like the casing, you should try getting another melodica. Look at the reviews on this site, and you will see what some of us think about different models. But if this melodica is in tune and you don’t like the sound, you may not like the sound you get from any melodica. Some melodicas have a better sound than others, but I have never heard an in-tune melodica that has a really bad sound. Even the cheapest melodica, if it is not badly out of tune, can produce a pleasing sound for those who like to play this instrument. As for the casing: all the best Hohner, Suzuki and Yamaha melodicas have a plastic casing. A wood casing is pretty, but it’s not something to worry about if you are just starting to play the melodica. Some of us have been disappointed in the best known wooden melodica, the Mylodica. It is very pretty, but in my opinion it is awkward to hold and does not have a better sound than my Suzukis or Yamahas.
My guess is that your melodica has an acceptable sound and should be adequate as a first melodica. I would play it without a mouthpiece. The sound is just as good without a mouthpiece, if not better. In my opinion, blowing directly into the end of the melodica provides the most pleasurable experience. And it encourages you to play without looking at the keyboard.