That's a good question.
1. 'Spree' is nearly always used in the way that you describe, in combination with a noun or gerund form. The contexts are also nearly always the two that you describe: either killing/shooting/ crime or spending/shopping/buying.
Although these are not compound nouns, strictly speaking, is very rare to use the word on its own. We sometimes use the phrase 'go on a spree', but it's usually clear from the context what kind of spree this is.
The sentence you suggested about the work isn't quite right, I'm afraid. We wouldn't use 'spree' in this way.
2. A 'xxx spree' is, by definition, a short and enthusiastic burst of activity. It refers to one single occasion. Obviously, if the tendency to go on sprees is in a person's character, you could say something like 'Anna goes on a shopping spree every time she gets her pay cheque', but you would still be considering each spree as a separate event.
I hope that helps.