Welcome to the forums! Sounds like you're not a total newbie, you've got a good handle on the pieces already.
If you could give a few more specifics to make sure we're on the same page, that would be great. When you say "downloaded strategy file" what do you actually have? Is it the compiled "control engine download file" (a single file with the extension .cdf)? Hopefully they gave you an entire PAC Control "archive" (a zip file with a number of files in it that make up your whole "strategy").
Either of those would require a controller to run (in a PAC-R like you mention, or one of our many other controllers, including the PC-based one we call SoftPAC). [Click here to see form 1677 that gives a full comparison of brains/controllers. For a higher-level overview try [URL="http://www.opto22.com/site/fd_snappac_components.aspx"]this flash interactive demo on SNAP components](http://documents.opto22.com/1677_SNAP_PAC_Controller_Brain_Comparison_Chart.pdf). The PAC-R is a special since it's both a controller AND and I/O unit, as you correctly indicated on your diagram.
Brains are not exactly simple I/O processors (they can run 96 PID loops, and do other I/O features like totalization & counting), but you're correct, they can't run a strategy. Also, those features are much easier to set up in strategy you've created (or inherited, which happens a lot) using our PAC Project Suite -- specifically PAC Control for the strategy.
On your HMI question, the short answer is: yes. Usually the tags created by your strategy (including those for I/O) are what's referenced in the HMI. However, our PAC Display (free!) HMI software also has an option to access I/O directly. We also have some (older) brains that connect to controllers via RS485. Guessing that's not what you're asking about, though.
FYI, our new groov Box also uses that same tag database to help you create browser-based (including mobile) HMI screens.
What HMI do you plan to use?
For your last question, assuming you have the whole strategy, you could open it in PAC Control and look in your strategy tree at the bottom under "I/O Units."
I'm guessing/hoping you'll see 2 there, one for the "local" I/O on your PAC-R1 (IP Address likely to be 127.0.0.1 meaning "talk to self"), and a second one for that EB1. The controller part of the R1 communicates with it's own I/O and the EB1 I/O in the same way (via the memory map, but you don't need to worry about that if you're using PAC Control).
Hope that helps get you going. FYI [training and [URL="http://www.opto22.com/site/support.aspx"]support](http://www.opto22.com/site/training.aspx) are free! We'd love to have you join a class here in Temecula, CA.