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.