As far as we're aware we have two options.
1. Take your computer offline before launching the game. Be aware you will need to login with your username and password. - You'll know you're offline if you have no network access.
You'll have an image like this:
on your start bar.
2. Launch Origin, go into the Origin Menu and select Go Offline. It will say offline mode in the upper right corner. -- Up by the minimize window button.
I am not fully sure about the gameplay questions. You may want to post them in Gameplay Help.
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I am not sure why one computer seems to behave differently than the other. That is something that would be best asked over at Answers.ea.com
As they maybe able to help troubleshoot the issue better. All we can do is share our experience we've had with the Origin software.
Origin Client/Web – Technical Support
https://answers.ea.com/t5/Origin-Client-Web-Technical/bd-p/origin-technical-issues-enThank you for asking about these questions over at answers.ea.com If you're having issues with their site you might try closing out the browser and clearing the browser cache and trying it again. If that doesn't work, try accessing their site with a different browser.
How to Clear Your Browser's Cache (wikihow.com)
https://www.wikihow.com/Clear-Your-Browser%27s-Cache#