1. Is there some way to understand whether running a particular script will lead to convergence without first running the geometry optimization.
You can do it for a static (e.g., initial) structure, performing a single SCF convergence test.
2. How to do a convergence analysis to understand best which parameter set will be best suited for faster convergence.
I think you just have to run a set of test calculations. I am not aware of any other for numerical simulations, in general.
3. Could you suggest some resource and ways to speed up a simulation (links to related articles will be helpful in understanding them in detail)
It is a very general question. One can always speed up calculations by doing more approximations, less accurate basis set, lower mesh cutoff and/or k-point sampling and so on. One can also try using more computer resources, but one should also check if using more cpus would truly speed up particular calculations, because in same case it makes no sense, e.g., for relatively-small systems modeled within LCAO approach and few k-points. But one should always consider the specific case to say something about it.
