WOW. I was expecting something dumb but this is next level dumb. You're basically forcing a 7 character password since I already know one of them is one of those three special characters. Then you've just given me like 5 more rules that limit what the password can be. Any password cracking service would crack this in hours. IT people should understand the basics about security before they are allowed to set policy.
Not exactly, because you don't know where the special character is. If the allowed characters are k, the number of 8-character passwords would be k^8. With this rule, even assuming that only one special character is used the number becomes 7^k * (3 * 8) = 7^k * 24, so if k ~= 60 the entropy is reduced by roughly 1 bit.
Still, it is an incredibly stupid rule.