How to test suspect gmail delivery problems?

[Josef Lowder]

Apparently gmail will not allow anyone to send a test email message to
themselves ... apparently not even from a separate gmail account?

So how can one test to see if a given email address or alias is working?

What other email/webmail options do not have this inconvenient quirk?

I'm about fed up with gmail.  One of the most annoying things is that
it is (apparently) impossible to create filters that will actually
delete (rather than just move garbage emails to trash).  This is
ridiculous.  I'm still getting 100+ garbage spams plus 100+ emails in
trash every day and I have to go through all these to make sure that
there is nothing in there that should not be; and almost every day I
find one or two items in both spam and in trash that should not be
there.  Valid items in "trash" are my error/responsibility because of
my aggressive filtering efforts.  This problem could be minimized if
not entirely resolved if I only had the ability to actually create a
"delete forever" filter for some of the most offensive garbage.

Is there any email/web mail service that allows one to create filters
that will either send an item to trash *OR* absolutely "delete
forever" those most offensive and repetitve nuisance garbage items
that keep filling up my email?