1. When a job offers says 'Contact directly' and gives a private (company) address, is there a way I can respond through Proz email so that I have my response on record with Proz site and not only on my private gmail account?
I am afraid this is not possible, since ProZ.com cannot keep a record of the e-mail messages you send directly from your e-mail account. A record of quotes is only possible when quotes are made directly via ProZ.com (i.e. when the contact method is "...submit your quote via ProZ.com...") and is available in the "My quotes" section under the Jobs and directories menu tab.
2. If I respond through my private gmail account to a job offer, can I refer the company to my Proz listing to view my CV or must I send it each time attached to my gmail message?
You can refer any client to your ProZ.com profile at any time. However, have in mind that some outsourcers may require that you send your CV attached to the email quote (perhaps because they do not have enough time to check profiles one by one). In such cases, it is recommended that you send your CV file attached to the email message, even when your CV is already available in your ProZ.com profile.
Please let me know if you have any other doubts or if you need any help.