1. What is the plural of index?
The plural of index is indices.
2. What are the other names for an exponent ?
An exponent is sometimes called a index or power.
3. Why is a dot sometimes used to mean "multiply" in algebra?
One of the reasons could be that if a normal multiply sign was used if could be confusing when using x as a variable.
e.g. x × x means x 'multiplied by' x. It is clearer if written x.x
Note it is NOT a decimal point.