I don't have any experience in this field. She does not have any friends. I don't have any milk. She doesn't have any money.

"Destitute" basically means poor, ie. without money. It's an absolute state. If you say "destitute of ___", then it sounds very poetic and tragic. We would never use that in regular conversation. "I am lacking experience in this field" is a little more normal-sounding.

Nope, doesn't sound natural to me at least.

destitute doesn't mean exactly 'poor' - it means without food or shelter or resources; being destitute and being poor tend to go hand in hand however. In fact you often see the phrase 'the poor and destitute'