Question 1

%% all the changes in this question were on the same issue - I did not
%% remember how to divide numbers and I wrote "a/b" in the test because
%% I wanted the teacher to understand my code
build_balanced_tree(1,t(nil,x,nil)):-!.
build_balanced_tree(0,nil):-!.
build_balanced_tree(N,t(L,x,R)):-
    N1 is N-1,
    N2 is N-2,
    %% I added these variables, and put the "div"s here and not in the lines below
    N3 is div(N1,2),
    N4 is div(N2,2),
    N5 is N4+1,
    (   N6 is mod(N1,2),N6==0,!, %% I changed this line
        build_balanced_tree(N3,L),build_balanced_tree(N3,R)
    ;
       (   build_balanced_tree(N4,L),build_balanced_tree(N5,R)
       ;
           build_balanced_tree(N5,L),build_balanced_tree(N4,R)
    )).

mirror(nil,nil).
mirror(t(L,x,R),t(NewL,x,NewR)):-
       mirror(L,NewR),
       mirror(R,NewL).

symetric_and_balanced(N,t(L,x,R)):-
    N1 is N-1,
    N2 is div(N1,2),%% I added this line
    build_balanced_tree(N2,L),
    mirror(L,R).

symetric_balanced_trees(N,Ts):-
    N1 is mod(N,2),N1==1, %% I changed this line
    N>0,
    findall(T,symetric_and_balanced(N,T),Ts),
    Ts\=[].