if you do not want ^F, then you can filter them out first using sed or tr.
eg sed -i 's/^F//g' file

then execute the awk command or you can substitute ctrl-f in awk. just an example only

Code:
awk '{sub(/^F/, "" ) } $0 !~ /name email/ && $0 !~ /=== ====/{print }' file
Note. press the ctrl key followed by F, not Shift-6 then F