Should questions in below form be on-topic?
Who is scholar X?
Can you introduce him briefly mentioning his areas of study, accomplisments and the books he written?
I think that such questions would easily fall under the closure category of "too-broad." I don't think there's anything wrong with specific questions about the lives of Islamic scholars, but open-ended questions like this one are of minimal use on SE.
I agree with Daniel's answer that such a question (in the form you described) would fall under "too-broad".
Who is scholar X? Can you introduce him briefly
If asked like this, it may be viable for some scholars, but others you might take as long as the introduction of some books which deal with brief introductions of it's author (from 5 pages to maybe 15 or more) I don't have any examples on hand.
If you ask
Who is scholar X? and what are his areas of study?
then this would be ok in my opinion, but may have longer answers for those scholars who are more well rounded.
If you ask
Who is scholar X? and what are the books he has written?
this may be fine for some scholars, but really I view such questions (especially in regards to some scholars) as a list question, which is not constructive for this site. So in conclusion, to ask about Ulama' is definitely on topic, but the question in the form you have described is multiple questions asked in, as well as too-broad.
I wrote an answer to a similar question where I felt that such things would be fundamentally on-topic, since knowing about the people who (claim to) represent Islam in the modern day is at least as important as knowing about the classical scholars. However, given that there's no real shortage of Islamic scholars out there (and on the Internet, literally anyone can say they're a scholar), unless it's for a very specific and obviously academic purpose (e.g. checking the credibility of a particular reference cited in an essay/book/fatwa/etc.) it's probably fair to limit it only to scholars who are actually so famous and/or prevalent that their history is actually relevant to the study of Islam (something à la Wikipedia's "Notability" requirements).
So, for the sake of extremes, scholars such as Shaykh Saalih Al-Munajjid or Imam al-Qurtubi, whose writings are readily found and cited on the Internet, would probably be well on-topic. However, the life history of the imam of your local masjid or the teacher of Islamic Studies at your local college are probably not useful to anyone except you.
Of note, I recently asked a question which covers exactly this topic, which I feel comfortably establishes not only notability but limits the scope well enough to not be "too broad": Who is Hafiz Salahuddin Yusuf? It's not seeking a full biography or life history, it just wants what makes him a credible authority in a widely-available edition of a major book of ahadith by a major publisher.