1.
           ______________________
          /     / 2  \  2   / 2  \         
         /     /______\____/______\
        /  3  /1/                  \
       /\    /\/                    \
      /  \  /_/                      \
     /    \/1/                        \
    /      \/           9              \
   /       /                            \
  /   4   /                              \
 /       /                                \
/_______/__________________________________\

3. Dan Rather, dominates, latter, peoria, treks, ancient, master, naples, trapped, cloisonne, sumo, disconcert, no u turn, fate.
The Andromeda Strain, tatterdemalions, proletariate, Perestroika, tennis racket, ascertainment, malapertness, salt and pepper, Indecent Proposal, mononucleosis, semiconductors, under construction, unfortunate, tar and feather.

4. Some notation: "abcd/efgh" means "Weigh the coins abcd against efgh".
"=:" prefixes the action to take if the indicating weighing resulted in a
balance.
"<:" prefixes the action to take if the right side was heavier
">:" prefixes the action to take if the left side was heavier
"<>:" prefixes an action to take on any imbalance
"(a)"  identify a as the counterfeit
"(abc)" the counterfeit is one of abc
"(>abc)" the counterfeit is lighter and one of abc
"(<abc)" the counterfeit is heavier and one of abc
"(<abc,>def)" the counterfeit is one of abcdef. If abc it's lighter, else
heavier

Here we go:
ABCD/EFGH
=: (IJKLM) ABC/IJK
     =: (LM) A/L
          =: (M)
          <>: (L)
     <: (<IJK) I/J
          =: (K)
          <: (J)
          >:(I)
      >: symmetric to <
The rest is probably the classic solution:
<: (>ABCD,<EFGH) ABEF/CGIJ
     =: (>D,<H) A/D
          =: (H)
          <>: (D) (actually, only > is possible)
     <: (>AB,<G) A/B
          =: (G)
          <: (A)
           >: (B)
     >: (>C,<EF) E/F
           =: (C)
           <: (F)
            >: (E)
>: symmetric to <

5. The trick is to make 4 levels of the same convex shape, and stack them.