Can pseudo random number generator generate all possible sequences?
If you are considering a pseudorandom generator that can work with seeds of any length, then the answer is "It depends". It depends on the pseudorandom generator. There are pseudorandom generators for which the answer is yes (e.g., $G(x)=x$, or any bijective $G$), and pseudorandom generators for which the answer is no (e.g., $G(x) = G'(\text{SHA256}(x))$, where $G'$ is a pseudorandom generator that accepts fixed-length seeds, is almost certainly such an example).

In practice, pseudorandom generators usually have a fixed-length seed.  In that case, if the length of the output is longer than the length of the seed, then there exists an output that isn't produced by any seed (of that length).  This follows from the pigeonhole principle.

In practice this almost certainly doesn't matter.  Usually what matters is whether the output of the pseudorandom generator passes statistical tests, or whether it is indistinguishable from true-random bits.