Fighting in the first couple months of a relationship is never a good sign, that is when people are still nutty about each other and think even the most annoying traits are endearing or cute or easy enough to ignore. If they're already fighting then I think they'll reach the conclusion they're not compatible in a relationship but they'll always be friends, which is what we've heard so many times. It makes sense, you can't get to know someone's true personality during an 6-8 week tv shoot, especially when you don't spend much time with that one specific person and you're dating over a dozen others at the same time.
I don't think Ed is used to having a fiance who expects him to always be reachable. Ed, there are only so many excuses you can use (the battery in my phone died, I left it at home, I turned the ringer off) before her suspicions grow totally out of control. Better answer that phone! This is not going to sit well with him, it'll turn him off in a big way. I get the impression he's the secretive kind of guy who doesn't like to be questioned about what he did, where he went, who he saw, etc. Even if he's just innocently hanging out with friends at the bar, he doesn't want to be pestered about it. JMO.