Translation:An introduction into her results and problems.
In school Physics our practical write ups had to include a section on sources of error and what steps you took to minimise those risks of error. I'm guessing that might be what they mean by "problems".
I agree that in English we say "An introduction to . . ." I can see why they've (erroneously) put "into" because the German is using "in" plus Accusative - but that doesn't make it right!! Good news is that I've seen in another post that "to" is accepted ;-)
Have there been any attempts thoughout the history of the German language to introduce separate words for "sie" (she), "sie" (they) and "Sie" (you)?
No, this is really only a problem for learners, not for native speakers. In fact, there used to be several different forms in Old High German. "siu" meant "she" and "they" (neuter), "sie" meant "they" (masculine), and "sio" meant "they (feminine), but they ended up being assimilated phonetically.
If you want to avoid confusion, you can use demonstrative pronouns instead of personal pronouns. That's what many native speakers do in colloquial speech anyway. Just note that this is considered rude when the people you're talking about are present.
Er hat ein Buch - Der hat ein Buch
Sie hat ein Buch - Die hat ein Buch
Sie haben ein Buch - Die haben ein Buch
Since there's no demonstrative formal you, "die haben" can only mean "they have".
For me, the idea makes sense (as a researcher), but it is not a complete sentence in English. For example, if a person were going to give a talk on her research, someone might ask, "What is she going to talk about?" A response might be, "She will give an introduction to (maybe into if a casual conversation?) her results and problems." In this case "problems" might be difficulty completing the research or it could mean possible error with her results.