What is worst case complexity of number field sieve?
The number field sieve has never been analyzed rigorously. The complexity that you quote is merely heuristic. The only subexponential algorithm which has been analyzed rigorously is Dixon's factorization algorithm, which is very similar to the quadratic sieve. According to Wikipedia, Dixon's algorithm runs in time $e^{O(2\sqrt{2}\sqrt{\log n\log\log n})}$. Dixon's algorithm is randomized.

All (heuristically) known subexponential algorithms require randomization. Dixon's algorithm needs to find integers $x$ such that $x^2 \pmod{n}$ is smooth (can be factored into a product of small primes) and "random", and the number-field sieve has similar but more complicated requirements. The elliptic curve method needs to find an elliptic curve modulo $n$ whose order modulo some factor of $n$ is smooth. In both cases it seems hard to derandomize the algorithms.

The nominal worst-case complexity of all these algorithms is infinity: in the case of the quadratic sieve and the number-field sieve you might always be generating the same $x$, while in the elliptic curve method you may always be generating the same elliptic curve. There are many ways around this, for example running an exponential time algorithm in parallel.