Yes. Each puzzle is checked so that exactly one way of filling the grid satisfies every row, column and box, so there is one right answer.
Yes. A puzzle is only used if exactly one filling of the grid obeys the rules. If removing a number would let the puzzle be solved in two different ways, that number stays.
Why it matters to you
With one solution, a puzzle can always be worked out by reasoning, and you can be sure that a finished grid with no repeats is the answer. There are no puzzles with two correct endings.
What it doesn't promise
One solution does not mean every step is obvious. Some puzzles need pairs or pointing, not just single numbers. The Sudoku solving techniques guide explains them.
What to do when you're stuck
Turn on pencil notes before you guess. The full Sudoku rules cover the grid and the one rule that governs it.