I performed p_mut_scan to see if certain mutants make the protein more stable. Is it absolutely necessary to run Relax (1) before running anything  like pmut_scan or ddg_monomer. I have already done about 6 months of work with these without Relax. Surprisingly, pmut_scan did correctly predict 2 mutants.
-> Do I have to redo everything since I did not relax the structure?
->Another question: What is the meant by "options_annealer" section in the documentation: " By default, fixbb uses the standard annealer used" 
Whether or not to run relax is depends on who you ask. Some people will say that it's always a good idea, and other will say that it's not necessary.
One of the things we have found, though, is that structures directly from crystal refinement (e.g. downloaded directly from the PDB) often don't score very well in Rosetta protocols. This isn't the fault of the crystallographers - it's just that the Rosetta energy function is sensitive to very small changes in atom positioning. Sub-angstrom changes which don't result in an appreciable change to the fit to electron density can cause a significant change in Rosetta score.
The issue with this from a design perspective, though, is that if you have a residue with such issues, Rosetta can often attempt to "fix" it by putting in "spurious" mutations (https://doi.org/10.1371/journal.pone.0059004). This is due in part to how the protocol is performed. If you do mutations on a fixed backbone, Rosetta isn't able to fix backbone issues when the backbone atoms are slightly off. As such, it might force a mutation to a different amino acid which better accomodates that backbone conformation, even if a slight, sub-angstrom backbone movement would have made the original amino acid more favorable. Pre-relaxing the structure prior to doing the mutagenesis eliminated this.
On the other hand, pre-relaxing the structure may pre-optimize and bias the structure toward the particular sequence you started with, as that sequence gets a chance to optimize the backbone, but other sequences are stuck with the fixed backbone. Often this is okay, as biasing a design to the "native" sequence is what you want anyway, but it's something to keep in mind.
I don't see any a priori reason that not pre-relaxing the structure would invalidate the results, so if you've done all the work with the non-relaxed starting structure, I wouldn't necessarily throw it out. But I would be cautious about your results and look at them with a critical eye. Are the mutation results you're seeing "real", or could they be an artifact of a poor starting structure?
Regarding the annealer, the annealer being referenced is the one which performs the Monte Carlo Simulated Annealing in the Rosetta sidechain sampler (packer). The default one is good for most applications, but we do have a selection of other ones which perform slightly differently for different use cases. (Most notably there is the "multicool annealer", which is more convergent than the standard annealer and can sometimes find lower energy structures.) For most purposes, unless you have a use case where you know that you want to try a different annealer, the standard one is fine.