On your question in title : no. Press 'I'key for inventory.
2nd question:yes, they share bank.
Attention Zenimax: Stamina builds don't hold up to magicka builds, and this is causing most of your class imbalance. It makes melee weapons and bows weaker than staves and class abilities. It makes medium and heavy armor less desirable than light armor. Fix this imbalance, and you'll address most of your balance issues.