Klondike is the solitaire everyone means by 'solitaire' — the one that shipped with Windows and taught a generation to drag cards with a mouse. Seven tableau columns, a stock pile to turn, and four foundations built up in suit from ace to king.
The tableau builds downward in alternating colours, so a red six goes on a black seven, and only a king can move into an empty column. Everything else follows from those two rules; the difficulty is entirely in the cards you can't see yet.
With perfect play and knowledge of every card, around 80% of one-card-draw deals are solvable. Playing normally, without seeing the face-down cards, most players win considerably less often — which is why it's still interesting after thirty years.
One-card draw turns the stock a card at a time so everything is reachable. Three-card draw turns them in groups and only the top of each group is playable, which makes the game substantially harder.
No — only a king, or a run headed by a king. That's why emptying a column without a king available wastes the space.