Sudoku has exactly one rule, and everything else follows from it. Fill the 9x9 grid so that every row, every column and every 3x3 box contains each digit from 1 to 9 exactly once. No arithmetic, no guessing.
The grid is 9x9, divided into nine 3x3 boxes. Some digits are given at the start and cannot be changed; the rest are yours to fill. A correct puzzle has exactly one solution, and it can always be reached by logic.
A digit may go in a cell only if it does not already appear in that cell’s row, its column, or its 3x3 box. If all three are clear the move is legal. Whether it is the right move is what the puzzle is about.
Notes let you pencil the candidates into a cell, which is how most players hold a hard grid in their head. Hints open a single correct cell when you are stuck. Neither is cheating: sudoku is a solitaire, and the only rule that matters is the one above.
No. The digits are only symbols, and nothing is ever added or multiplied. Sudoku is pure logic and would work just as well with nine different colours.
A properly made one cannot. Every puzzle here is generated with a uniqueness check, so there is always exactly one answer.
No. If you are guessing, there is a deduction you have not found yet.