Why in RSA do we use mod n rather than mod phi(p⋅q)? When we pick $e$: $$e \in \{1,2,3,4,...,\phi(p\cdot q)-1\}$$
where $\gcd(e,\phi(p\cdot q))=1$. Similarly when computing $d$ which is the modular inverse of $e$ (the private key) we use the extended Euclidean algorithm as
$$\operatorname{EA}(e, \phi(p\cdot q))$$
so that $$e\cdot d \ \equiv \ 1\pmod{\phi(p\cdot q)}$$
So having a message $X$ why does simultaneously encrypting and decrypting message as
$$ {(X^e)}^d \equiv  X \pmod{\phi(p\cdot q)}$$
not work, as it should be equivalent to $X^{e\cdot d}$ and $e\cdot d$ are the inverse of each other in the set of  $\{1,2,3,4,...,\phi(p\cdot q)-1\}$ so they are supposed to cancel each other which is supposed to be the idea of RSA.
I know that $e\cdot d$ result in plaintext to be decrypted to 0.00 if I follow the normal encryption/decryption process (since I tried it)
Can anyone explain why it does not work as described?
There are two reasons for not using $\varphi(n)$ during encryption.
The first one is that it doesn't work - you can verify this by looking at the RSA correctness proof. It requires, that the modulus is $n$.
The second one is - if you know $\varphi(n)$ you can efficiently compute $d$ given $e$, and therefore know the private key.