Yes, you should read Michael Barr's article on memory testing.

It gives a thorough description of the types of failure that you are testing for, and a thorough test method.

Simple "write-and-read-back" routines are of little practical use as they are easily fooled...

As to clearing memory, the only way to do it is to visit each & every location and write your desired "clear" value to it.
(unless your RAM chip happens to have a "reset" pin of some sort...)