Yes you can. Use HM Rock Smash in the following places;
Ruins of Alph: Helix fossil (Omanyte) and Old Amber (Aerodactyl)
Cliff Cave: Claw fossil (Anorith)
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you cant
You use rock smash and can sometimes find fossils.
in pewter city, the museum has a guy that will restore fossils your mother(sry i mean your father)
You can only get the Helix Fossil in Pokemon HeartGold. This means that to get an Omanyte or Omastar in SoulSilver, you must either trade for one or trade for a Pokemon holding one.
There is no best Pokemon on Pokemon HeartGold.