I have an account in an mail server with email address eg. email@example.com but it does not allow sending more than 100 mails per day. Can I use postfix server to send mails on behalf of firstname.lastname@example.org
Postfix is a back-end email manager, like Exchange Server or Sendmail and not a front-end like Thunderbird or Eudora.
You may wish to also consider why you want to violate your terms/contract with your ISP.
Also, setting up another email server may not be as easy as you think. Yes, the technical software of an email server is easy to get and install, but email follows definitions bound in DNS records (specifically the MX record) and a number of us system administrators check each email message, and look for a defined MX record. If you don't have a valid email server address, and other pieces put into place, your message gets marked as spam, and eaten. If you do too much of this, other consequences, such as being blacklisted by an organization, can get you into real trouble.