Must all the values in the same column of a relation have the same length?

No it is not necessary for a column in a table to have the same data when speaking of the length of the data. There are no restrictions on the length of data but the all the cells of the column must have the same data type. As an example, we can have a look at the bellow tables. In this table the Manager and allowance tables have data with different length but same data type i.e. strings and integers.

Managers Allowance
John 100
Shepard 500
Will 1100