It has both modes. At the top of your feed, there's an icon that looks like three sparkles. If you click it, you can set your feed to "Home" (the Facebook-ish option where an algorithm creates your feed) or "Latest Tweets" (the linear timeline).
It is, yes. "Following" is the same "Latest Tweets" chronological feed. I just confirmed it on my device to be sure. (by scrolling a large distance several times and checking timestamps)
Surprisingly little known, but Twitter also has a strict-timeline mode. It's great! Tap the pair of stars in the upper-right to bring up a menu to turn it on.
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