what is the reference to Google Apps? you are saying here that you access your three GMail Email Accounts from GMail on the web (presumably on your computer) and you access these three email addresses on your iPhone using the GMail app?
Yes, I use Chrome browser from several computers to manage several gmail accounts and I use the Apple Mail app from my iPhone for those same accounts. The only real difference in a Google Apps account is simply that it has a real domain name associated. On the iPhone is where I use the app specific passwords.
how you use the Google Authenticator? i seem to use this nicely when i get a PROMPT for something from GMail but if i try to use this generated password in MAC MAIL or in SPARROW or something else it does not take
Google Authenticator codes are used for logging in through the browser only. A given code changes ever minute and can't be used for mail clients.
Google app specific passwords are still used for any mail client like Apple Mail, Sparrow, Thunderbird, Outlook, etc. on Mac OS. App specific passwords are also still used in Mail on iOS. App specific passwords do not expire like authenticator passcodes and therefore you don't need to change email client passwords after they are set up. You should use a different app specific password per device because you can cancel a single app specific password at any time if you were to have a lost iPhone for example.
The Google single use passwords are ONLY ever used if something goes really wrong and you don't have you iPhone and therefore can't generate an authenticator code when needed to login to webmail.
OK. i caught that Send As option at one point. this is if you log into the website, yes? also, the Filters means that you color individual EMAIL ADDRESSES in GMail website and then you can easily see which email in the UI was sent to which email address?
Yes, login to a Google account through the browser and click the "Cog" > "Settings" > "Accounts" > "Send mail as". In that section you can add your other email addresses that you may want to send mail as right from this single Google account. Once set up (and confirmed) you will be able to choose a "From" address when in the compose dialog.
Yes, you can set up a Google "Label" for each email account that you are forwarding in. Then, set up a "Filter" that applies the right label to all incoming emails from that account. You may then need to go into the label display settings and make sure that all your lables are displayed on the sidebar. The easy way to learn filters and lables is to try creating a label for a specific person you get email from and then create a filter to apply the lable to all of their incoming emails.
Lables are simply categorization tags that allow you to quickly query a specific set of email in your Google account. There are no real folders of any kind in Gmail, just labels. Clicking a label in the sidebar simply executes a databse query to display only those messages. The other benefit is that you can change the colors to have a visual que for messages with one or more lables applied as well.