I personally do not believe long distance relationships work, and cheating just happens. I need the physical contact, I need the cuddles and the forehead kisses. I'm sort of a believer in open relationships for long distance, as long as you promise not to ever tell the person what happened when you get back together, but I mean, it's some tough shit.
As for signs they're cheating, I falsely accused my boyf of cheating mainly because my mum was cheated on and I was sort of sceptical from the beginning. I'd say, when they have things in their room, like a guy having a lipstick. My boyfriend had a headband, and i was about to catch him out on it until I noticed him using it to wash his face.... he legitimately bought it for that purpose. When they don't let you read their phone, or always seem to have their messages deleted. When they stop making effort to hang out with you but they make effort to hang out with other people.. when you call them and there's voices in the background, when their stories don't make sense, i.e says they were with their friend, but you ask their friend and they deny ever seeing them. Things like that.