Kim, this is a very interesting question that you have asked and I am certain that there will be other readers of the Women24 Careers website who have been faced with similar requests after an interview.
I will answer the second part of your question first. It is always important to have good contactable references in your CV – these would be people who can attest to your competencies and expertise in your current or previous work situations. They would also to speak about your work ethic, your commitment and your relationships with clients, management and fellow-colleagues. This potential employer is dealing with this part of the selection process very well as they are advising you that as a short-listed candidate they now wish to move to the next stage, namely contacting your references to gain a greater insight into you and how you would or may “fit” into the new organisation. it will also afford you an opportunity of advising your references that you have applied for a new position and that they should expect a call from the “new” company.
I am not altogether certain what is meant by the phrase “cost of employment” – I am presuming that the employer would like to see your current salary and remuneration package. There is nothing inherently wrong with this approach, but my feeling is that a potential employer should not be comparing your current salary with a salary that they wish to offer to you. I feel that they should rather make an offer to pay you a salary commensurate with your qualifications and experience – and then leave the decision to accept, reject or negotiate the terms and conditions of your employment package. But, as I said at the outset (and if this is what is meant by the phrase), this would be a personal decision.
This is a broad sweep through your question – please do submit another question to the website if you require any further assistance or information.
Good luck with your future endeavours!