Hi Jason, I totally forgot about this issue, now I'd like to solve it properly.
I looked into the situation again, then I noticed magic_quotes_gpc was not turned on all this time.
So I turned it off from .htaccess and it seems it's working this time finally, as now the texts entered on contact form with double quotes marks are passed perfectly to confirm page (without back slash, with double quotes marks.)
After this is the problem though. The email sent is missing texts after the first double quotation.
What could you suggest to solve this?
I attached confirm page php file just in case.
Thank you for your help.