This is NOT a moveset suggestion question.
No, it cannot.
Icicle Spear- learn at level 13 as a shelder
Spike Cannon- learn at level 40 as a cloyster
Twineedle- you need to breed female scorpi/drapion with male beedrill/escavalier who knows twineedle for a male scorpi who knows twineedle. Breed the male scorpi with a female cloyster/shelder for your final pokemon.
Rock Blast- you need to breed a male omante/omaster or corsola or anorith/armaldo with a female cloyster/shelder. There are no pokemon that can learn both rock blast and twineedle and breed with cloyster :( You need to choose one.