Thanks, Ondrej and Ian for the very useful information.
A quick followup contribution, now that I understand what's going on and what to
look for:
When querying and only returning one row (see the second part of my original
message), the following appear to be equivalent:
$prep_query="SELECT daterequested,datecreated FROM accounts where
username='$username'";
$query=$dbh->prepare($prep_query);
$query->execute;
($daterequested,$datecreated)=$query->fetchrow_array();
and
$prep_query="SELECT daterequested,datecreated FROM accounts where
username='$username'";
($daterequested,$datecreated)=$dbh->selectrow_array($prep_query);
or you could even go the extreme and put the query in quotes in the parentheses
after selectrow_array.
Once again, thanks for your input!
Pete