I'm not sure what is being attempted here. I also haven't synthesized a Wittig reagent before, so I am only guessing. I don't see why K2CO3 would have been added. This is what I would expect. If you were to react triphenylphosphine with the bromoalcohol, it should form the phosphonium salt. I am guessing this may be insoluble in the acetonitrile, but I don't know that. If it were insoluble, I don't know why potassium carbonate would have been added as it too would be insoluble. At this point, it would be a mixture that I would not want.
Re: mechanism, this should be a simple SN2 substitution reaction.
Perhaps someone with experience in preparing phosphonium salts for Wittig reactions could provide some help here.