Every equation must contain a term! In fact it must contain at least two.
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It is an equation. It could be an algebraic equation, or a trigonometric equation, a differential equation or whatever, but it is still an equation.
No. In the variable x, alone, it is linear. In the variable y, alone, it is linear. But taken together, in x and y, you have a term which contains xy - that is, a term in which the powers of the unknowns add to 2. So the equation is not linear.
The quadratic formula cannot be used to solve an equation if the coefficient of the equation's x2-term is 0.
an equation that shows how to calculate the value of the next term in a sequence from the value of the current term