Broken bathroom scales may be reliable, just not accurate. There are dozens of studies clearly establishing NTD validity. Moreover, a series of independent reviews provide support for their validity. Most recently, a meta-analysis of NTDs concluded that average validity may be on the order of .5. That is correct.
False positives are a function of instrument validity and the base rate of a phenomenon.
Yes, but that criticism is misplaced. Or, alternatively, if there is such a cost, it is not one properly borne by the institution. The Employee Polygraph Protection Act essentially banned polygraph use for private sector pre-employment selection. Perhaps, but on advice of counsel, I strongly suggest that you don't tell them. Your institutions routinely decline to provide this information.