References related to Chengchuan Liu's Project 

paper #1:
[55] RakhimovEtAl CommAlg 2010 34pp (here)

Review of [55] (here)

A paper citing [55]:
[59] RakhimovEtAl IJAC 2011 15pp (here)

Review of [59] (here)

Another paper citing [55]:
On derivations of some classes of Leibniz algebras
Rakhimov, Isamiddin S.; Al-Nashri, Al-Hossain; J. Gen. Lie Theory Appl. 6 (2012), 12 pp. (here)

Review of:
On derivations of some classes of Leibniz algebras
Rakhimov, Isamiddin S.; Al-Nashri, Al-Hossain; J. Gen. Lie Theory Appl. 6 (2012), 12 pp. (here)

paper #2:
Central extensions of null-filiform and naturally graded filiform non-Lie Leibniz algebras
Adashev, J. K.; Camacho, L. M.; Omirov, B. A.; J. Algebra 479 (2017), 461-486. (here)

Review of
Central extensions of null-filiform and naturally graded filiform non-Lie Leibniz algebras
Adashev, J. K.; Camacho, L. M.; Omirov, B. A.; J. Algebra 479 (2017), 461-486. (here)

Questions related to Chengchuan Liu's Project 

Question on October 9 "Can you clarify the defintions of filiform and grL in [55]?" (my answer here)

Questions on October 17 and my answers
1. Do I need to care about the proofs of Theorem 2.1 and Theorem 2.2 in [55]?
ANSWER: NO. They are proved in other papers and stated here for reference.
2. Theorem 2.1 says a complex (n+1)-dimensional naturally graded filiform Leibniz algebra is isomorphic to NGF1, can I say that this algebra will not be isomorphic to NGF2 and NGF3?
ANSWER: In Theorem 2.1 it is stated that the three types are non-isomorphic.
3. From the definition of G_ad, G_ad is a "closed subgroup of GL(V)", so does it mean that all five isomorphisms are group isomorphisms?
ANSWER: GL(V) is the set of invertible linear transformation of the vector space V. So every element of GL(V) takes a basis to another basis. G_ad consists of those elements of GL(V) which take each adapted basis to another adapted basis. GL(V) is a group under composition of linear transformations (See your question 4). G_ad is a subgroup. (you can ignore the word "closed") For the definition of adapted basis, see definition 3.1 and theorem 2.5 in [8], which is attached. To answer your question, all elements of GL(V) are isomorphisms of the abelian group consisting of the vector space V under addition of vectors, so in that sense the answer is yes.
4. In Proposition 3.1, what is the meaning of the circle? I guess it acts as the same function as f(g), but I don't know if this is correct.
ANSWER: Yes, you are correct. It is composition of linear transformations (we have called this multiplication of linear transformations) (reference [8] here)