Kohen and divorcee

Question

1. If a Kohen is civilly marrid to a divorcee and they the become religious, is it possible for them sto stay together with her as his pilegesh (since according to some, the issur is only if there is kidushin)? 2. Why do we assume that companies who have both kosher and non-kosher thoroughlyclean things between the runs so that any remaiing non-kosher is less than 60. I would think that on occasionn it might be more than this. Is this something we should ever be concerned about (and if not, why not)?