What about writing for readers that include children?
"#$@&#%#*!"
Can symbols be used to denote foul language in dialog? For example, he said, "#$@&#%#*!"
If so, exactly which symbols are appropriate?
What about writing for readers that include children?

Heck, my 8-year-old has heard it all before. He lives with me, after all.Seriously. I bet any twelve year old knows more swear words than I do and I know a lot.
Using this stuff to denote profanity:
@#$%&
is a longstanding convention dating back to the 1920's or earlier. It's only ever been used in some comic books and many newsprint strips. The whole point of doing this is that those two mediums are generally not allowed to use the actual profanity (comic books can now adays, but newsprint is still vastly limited), yet still need to somehow suggest the profanity. And given the limitations of word balloons, that is the best they can do.
If you are doing an actual comic book or a newsprint comic strip, go ahead.
But I am under the impression that you are NOT writing for either a comic book or a newsprint comic strip. I am under the impresison you are writing for an actual book.
A book is an entirely different medium than comic books and newsprint comic strips. No book would ever use those symbols to denote profanity (unless the book was a hardbound compilation of old vintage comics or old vintage newspront comic strips). So the answer is that you CANNOT resort to using those typeset characters because it simply isn't done.
You can SUGGEST profanity via the conventions of the novel form in a way that neither comics or strips can. The richness of novel prose has so much more wiggle room for that sort of allusive suggestability than comics and strips. The skill of the writer comes into play here. So show us the range of your skillfullness.
I did in my comic because Hagar said it was #%&*^$@#! fine if I wanted to do it.Can symbols be used to denote foul language in dialog? For example, he said, "#$@&#%#*!"
If so, exactly which symbols are appropriate?