Vagabond and neo have some really good points.
(Aside from wanting to "control" a woman." ...

So I think what you're looking for in a girl what determines the "line" for her to cross. If she's just a Gf, and you's are dating, ok, I'll agree it's nothing serious.
But if it's someone you're in love with (and SHE'S in "love" with you) then different rules apply. In my opinion. Like, gawking at other guys, liking there pics, etc. I don't think it's "AFC" for you to be upset with someone for liking someone else's pics or flirting with other guys if you're in love. It's a red flag like neo said.

How can you find out if she's talking to other guys, cheating on you, and sync if your in a relationship.
And what are some other red flags.

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I'd say even if you're just dating a woman, it's disrespectful for her to gawk and flirt in front of you. If I was on a first date and a woman gawked or flirted with another guy, it shows a lack of respect. If you went on a first date and gawked at a woman during it, or flirted with the waitress, wouldnt the girl you went out with rightfully think you're a jerk?

As to social media, comes down to whether her actions show she's interested in someone else. I know girls who click like on a ton of things; so if she's one of those girls and clicks like on different people's stuff the no big deal. If she's having long wall convos or only messaging certain guys then could be a flag.