Those port are for:
25: incoming mail. So, if you expect to receive email from other mail servers, yes it needs to be open.
80: http. If you have web sites, yes it needs to be open
443: Secure web. If you use webmail, it needs to be open (or any other app that requires https:)
To trouble shoot your mail problem, has your ISP started blocking outbound SMTP connections? Mine did this a couple of years ago, forcing you to use there SMTP server to relay your mail from. To test this, make sure SMTP proxy is off on your server, then try and telnet to port 25 of someone's domain (you can use mine to test if you want "brummell.net"). If you don't get a respones it's a good probablility your ISP has started blocking port 25 outbound. If you do get a response, I have no idea why your server is not sending mail. Maybe the logs will tell you more as to why conections are being refused.