"You agree that EA may collect, use, store and transmit technical and related information that identifies your computer (including the Internet Protocol Address), operating system, Application usage (including but not limited to successful installation and/or removal), software, software usage and peripheral hardware, that may be gathered periodically to facilitate the provision of software updates, dynamically served content, product support and other services to you, including online services. EA may also use this information combined with personal information for marketing purposes and to improve our products and services. We may also share that data with our third party service providers in a form that does not personally identify you. IF YOU DO NOT WANT EA TO COLLECT, USE, STORE, TRANSMIT OR DISPLAY THE DATA DESCRIBED IN THIS SECTION, PLEASE DO NOT INSTALL OR USE THE APPLICATION."
Full EULA
That's part of the EULA you signed when installing Origin I'm afraid. What's EA's answer for those who don't want to be snooped on? "Don't install it." No seriously, that's their answer.
DRM is getting very invasive these days and it's not just EA doing it. I recently bought the game Anno 2070 from Ubisoft and one of its' caveats regarding DRM is that you can only install it three times. Now you might think that's reasonable or not but what's really jawdropping about it is that if you install it on your computer and then upgrade your graphics card the DRM treats that as a new computer and lops off one install.
Unless you want to pirate a game to circumvent all this DRM (rather ironic in itself) you're stuck with it. Well there's always
Good old games
Edit - Forgot about the seeing what a process is accessing part.
First thoughts would be to use Process Monitor which you can download from:
http://technet.microsoft.com/en-us/sysinternals/bb896645
You should be able to filter by the process you want, in this case Origin, and it'll display what files it's accessing.
Note - I don't have Origin so I can't confirm this but I tried it out with the notepad process and here's what I found.
First you need to filter the results in Process Monitor. Easiest way to do that is to get the PID (Process ID) which you can find by opening up a command prompt and typing 'tasklist' which will display currently running processes. Find the right name and take note of it's PID - for my notepad process it's 3080. Create a new filter in Process Monitor and select PID is 3080 and apply. You should now have a list of file paths that the process is accessing.
I'd actually be quite interested to know what Origin is accessing as well if you try this yourself.
Also you can open up that dmp file (I'm assuming you mean you created a dump file by right clicking Origin in process manager) by downloading windbg from:
http://msdn.microsoft.com/en-us/windows/hardware/hh852363
When installing just check the Windows debug tools. The other options aren't needed for opening a dump file. After it's installed just open it up and go to Open Crash Dump in file. You need to know the file path but that should be displayed when creating the dump file. However you can view the default location by opening up control panel -> system -> advanced -> startup and recovery and then it should show you where dump files are saved.