Is it possible a state be a Quantum Spin Liquid and has long range order at the same time?

The characteristics of QSLs are very much an active area of research. I am not aware of any argument which would guarantee that (2) + (3) implies (1). However, in systems with half-integer spin, it is well accepted that (1) implies (2) which in turn often leads to (3). Here I paraphrase the argument from Section 5.1 of the review article by Savary and Balents (Rep. Prog. Phys. 80 (2017) 016502):

1. The Lieb-Schultz-Mattis theorem (and extensions/generalisations thereof) implies that in the thermodynamic limit, a system with half-integer spin and an $SU(2)$ invariant Hamiltonian must have either a gapless excitation or a ground state degeneracy.
2. If one can realise a state of this system with no spontaneous symmetry breaking (no long-range order), then it cannot be a topologically trivial quantum paramagnet (the "typical" magnetically disordered state), since this is fully gapped and has no ground state degeneracy.

The authors point out that on a torus, the case with ground state degeneracy implies topological order (the toric code is the typical example of a highly-entangled QSL with emergent anyon excitations). The other interesting point is that if there is a gapless excitation in the disordered phase, it is not a Goldstone mode, and so must exist due to non-trivial topology.

I hope this at least partially answers your question.