Your sentence 3 is a totally commonplace / acceptable variant of sentence 1.
Sentences 2 and 4 are a more complicated case. I am not actually convinced sentence 2 is a sentence, which means it is rather odd to encounter it from a reputable TEFL source. It appears to me a sentence fragment. Perhaps somebody else can think of another reading whereby it is a fully-fledged sentence in its own right, but at the moment I can't.
Your sentence 4 has the same property, but this is obviously not your "fault" since it is like that in the original sentence.
However, the other change you make by removing "up" is a problematic one. To dig something is, idiomatically, to enjoy it or condone it. The phrase is strongly associated with hippies and counterculture of the 60s/70s ("Can you dig it?"), but still in occasional use today. Although the context makes it plain that this meaning it not intended - a detective would not be sitting around going "this is great info about the employee, I dig it", unless that detective was Shaft - it still makes the sentence somewhat awkward, and essentially forces the listener to complete the "dig up" idiom by mentally adding the "up".