Yes, algebra uses abstract symbols to represent concrete elements in the real world.
No, in an algebraic equation, the same variable cannot represent two different unknowns.
Yes, many great mathematicians were also philosophers.
No, An algebraic expression doesn't contains an equal sign, but an algebraic equation does.
No, if the expressions are in the same set. Yes, if they are not. (The same variable can represent two different unknowns in two different algebraic expressions.)