The essense of the solutions:

Q1: A |- x : A(x)      
 
    A[x:u] |- e : t
    ---------------------------   l in s
                          s
    A |- lambda^l x.e: u ---> t


                  s
    A |- e_1 : u ---> t     A |- e_2 : u
    ------------------------------------   where s ranges over sets of labels,
           A |- e_1 e_2 : t                just like u,t range over types,
                                           and e_1,e_2 range over expressions.

Q2: No.  

Q3: Fix some type u.
    psi(t) = (t* -> u) -> u
    int*   = int
    (s->t)*= s* -> ((t* -> u) -> u)
    Gamma({x:t,...}) = {x:t*,...}

Q4: {2,3}.