Oftentimes Vietnamese people pair two synonyms or two words that are similar by association for added emphasis or to transform it into a noun.
e.g. bơi and lội both mean to swim but bơi lội means swimming.
e.g. nhanh and lẹ both mean fast/swift/quick but nhanh lẹ is more emphatic.
In the case of xây and xây dựng, xây = to build/construct and dựng = to erect/to place upright. You would say "chuyên ngành xây dựng" for the construction industry, however, to ask "what are you building?" you'd use "bạn đang xây cái gì?"
"Làm" for make? A subtle difference with no context and with it could be a big difference.
No, that would be read as "tu chỉnh" in Sino-Vietnamese. Xây dựng would use Vietnamese characters. Xây is 土+差 while dựng is 立+孕.
As a student of Chinese for many years, I love having not only the Sino-Vietnamese readings but also the Vietnamese characters. Thank you!