Regarding sending automated notifications to email (instead of as SMS to cell phone)... The notifications are currently also being sent to email, but I get a ton of emails and I don't want to check email constantly, nor do I want to eat up data checking ALL emails.

It would be helpful if I could send important emails to a GMail folder (label), then set up iPhone 'Notifications' to pop-up Alerts and show Badge App Icons for that folder (label) ONLY, but I haven't figured out how to do that, either.

You could probably use IFTTT and something like Pushover to accomplish this.

What if I don't use a local SIM and just want to forward from GV to my AT&T phone when traveling internationally? Will GV forward texts internationally?

If I want to text a response, I gather I will pay AT&T the usual rate for outgoing international text and MMS.

That will work, since your GV is just forwarding to a US phone number.

I think it should also work for forwarding texts to your US phone number. It's AT&T's job to see that the text actually finds you.

Google Voice Is Great
 

In the US, I only give out my good voice number. Since I travel frequently I know I can get my voice mails and texts anywhere. Also with google voice coupled with gchat I can place and receive calls on my computer as long as I have gmail open. I have an iphone 5 I travel with and I routinely use the app to text people in the states. Unfortunately, it will not let you call directly from overseas. I couldn't function without it.

When traveling internationally just use the google voice app. I find it is a lot more reliable and cheaper than having messages forwarded.