Shake256 Infinity Collision Two diferents inputs can have the same output in $Shake256$ for every output size (for example, $Shake256(input_1, \ell) = Shake256(input_2,\ell)$ for every $\ell$)?
Two diferents inputs can have the same output in $Shake256$ for every output size (for example, $Shake256(input_1, \ell) = Shake256(input_2,\ell)$ for every $\ell$)?

Yes, it is possible.  In fact, it is inevitable that some such pair $input_1, input_2$ exists.
Shake256 maps the input into a 1600 bit state, and then converts this state into an arbitrarily long sequence.  If two different inputs map to the same state, then they're produce the same sequence (independent of how much output you ask for).
In particular, if we consider all 1601 bit inputs, there must be (by the pigeon hole principle) two different inputs that map to the same state; that observation gives us an upper bound on the required size of $input_1, input_2$.  Almost certainly much smaller pairs exist.
Now, finding such a pair, well, that's a different (and far more difficult) problem...