If you are experiencing a problem others are not ... first you should UPGRADE and see if the problem goes away, as many of these bugs have already been eradicated. Upgrading Vicidial is fairly easy and not a bad idea as a "first reflex". You are working with an earlier release, the community is working with 2.14 with daily updates/upgrades. Bugs are not ordinarily fixed in previous releases, but in the development/community version. Upgrade!
1) Please don't take this the wrong way.
2) Seriuosly. But here we go:
3) You have the earmarks of a "very smart person" and may at some point outsmart yourself in the Vicidial arena. My BEST advice to you is to (at your next sign of trouble, or now in preparation for that trouble ...) reinstall your system with Vicibox.com's .iso installer if you can. If you have some sort of restriction that blocks your ability to install from an .iso, use Stock CentOS and the instructions available at Goautodial.com, then upgrade as soon as you're finished and you should have a stock/stable universally used system (not as universal as the Vicibox installer, but close).
Vicibox.com has a PDF for installation, Goautodial's site has a Wiki.
After installation, switch to the Vicidial Manager's Manual for configuration.
4) Yes, I realize you probably know most of that already, but I've seen a lot of very smart techs ... battle for weeks with arcane "installation specific" bugs that were generated by their specific installation method.
That being said: Yes, browser-specific bugs are fairly normal in the linux (and thus vicidial) world when we're talking about websites with specific behavioral issues. Vicidial's Agent Screen is ... special. It's also the cumulative work of thousands of production hours designed to cover virtually every call center on Earth's needs. So it's got its reasons for specialness.