Question

Is Page.IsValid and args.IsValid depend each on other?

I mean if args.IsValid=”true” the Page.IsValid must be “true”.

And ofcourse conversely:
if Page.IsValid=”true” so args.IsValid=”true”

Answer 1

Page.IsValid (readonly) returns true when page validation succeeded; otherwise, false.

Read MSDN doc.

For this property to return true, all validation server controls in
the current validation group must validate successfully. You should
check this property only after you have called the Page.Validate
method, or set the CausesValidation property to true in the
OnServerClick event handler for an ASP.NET server control that
initiates form processing.

In ServerValidation handler; You may set true or false to ServerValidateEventArgument.IsValid property if input validation (args.Value) is succeed or failed respectively.

MSDN Doc

Once your validation routine finishes, use the IsValid property to
indicate whether the value specified by the Value property passed
validation. This value determines whether the input control associated
with the CustomValidator control passed validation.