I want to know what 천룡학당 mean and what's the difference with 천룡무관? I believe 천룡 means Heavenly Dragon but what is 학당 and 무관?
학당 is an archaic term for "school" (학교). The modern counterpart will be called 학교, or maybe 학원 if it's not a part of standard curriculum (e.g., a ballet school for children will be called 발레 학원).
Off the top of my head, I can't think of an archaic English term for "school", so simply translating it to "school" seems good enough to me.
jick posted a good answer on 학당. Although the phrase 한국어 학당 (韓國語 學堂, a Korean language institute) is still used, I agree that 학당(學堂) is an old-fashioned word meaning a school or educational institution. You can find 학당 in the standard dictionary.
You mentioned both 천룡학당 and 천룡무관, so it is obvious that the author contrasts 무관 with 학당. As you know, this kind of contrast is common. For example, the word 문무(文武) can be translated as (the arts of) pen and sword. I would say that 학당 relates to pen while 무관 relates to sword (Of course, some types of martial arts do not use weapons).
Because you are reading martial arts fiction, you should note that one can combine Chinese characters to coin a word. 무관(武館) is just one example of such a word. If you know any relevant words, such as 무도관(武道館) and 연무관(演武館), you can easily guess the meaning of 무관. Otherwise, you have to do it using the meaning of each character: 무(武) and 관(館). Thus, 무관 is interpreted as the place where you learn and practice martial arts.