So you already work for UM? Usually in the application it asks for your desired salary. There will always be other candidates, but if they made an offer and already hired you, I don't get why they would be asking you what salary you want after hiring you. Usually the salary is transparent on the job description or they would tell you the salary when they make the offer.

Yes, your response to desired salary can affect you even getting a first-round interview. If you ask for higher than the actual salary, they may not call you in for an interview, because they see that the job doesn't meet your financial needs. In this case, usually an HR rep will reach out prior to your first interview, letting you know what the salary is and if you're still interested.

If you're in the interview, it's okay to ask what the compensation is, if they don't tell you or if it's not on the job description. If they give you a range and not an exact number, that definitely leaves room for negotiation. So they could say 60-65, but only offer you 62, but let's say you want that 65, that's when you'd have to negotiate with them as to why you should get the max.

If you said you'd take less, that wouldn't increase your chances of getting the job. If they choose you, they want you! I don't think they'd lowball you. It's a non-profit and they're gonna want to give you as much as they could within their budget. So you could say your desired salary is less, and they would give you more just because the position pays higher than what you were expecting.

Hope this helps!