Squatting is mating behavior.
It's also an instinctive submission reaction/behavior that has nothing to do with mating.
She's way too young to be squatting for sex...she may have been startled.
She us probably the second in command, my alpha chicken was picking on my newest chicken so I separated the alpha, so now this one would be the new alpha
Just because a bird is picking on another doesn't mean she the 'alpha'.
Separating a bird that is 'picking on' another may help the situation ...or not.
There is pecking all down the pecking order line, it's a normal communication behavior.
Extreme pecking can have several causes...lack of space and feeding stations would be the first things to look at. As long as there's no copious blood drawn and/or new bird is not trapped/pinned down and beaten unmercilessly, let them work it out. Every time you interfere or remove new birds, they'll have to start the pecking order thing all over again.
You just added a new bird(just one?), how did you integrate/introduce that new bird?
Here's some tips on....
Integration Basics:
It's all about territory and resources(space/food/water).
Existing birds will almost always attack new ones to defend their resources.
Understanding chicken behaviors is essential to integrating new birds into your flock.
Confine new birds within sight but physically segregated from older/existing birds for several weeks, so they can see and get used to each other but not physically interact.
In adjacent runs, spread scratch grains along the dividing mesh, best if mesh is just big enough for birds to stick their head thru, so they get used to eating together.
The more space, the better. Birds will peck to establish dominance, the pecked bird needs space to get away. As long as there's no copious blood drawn and/or new bird is not trapped/pinned down and beaten unmercilessly, let them work it out. Every time you interfere or remove new birds, they'll have to start the pecking order thing all over again.
Multiple feed/water stations. Dominance issues are most often carried out over sustenance, more stations lessens the frequency of that issue.
Places for the new birds to hide 'out of line of sight'(but not a dead end trap) and/or up and away from any bully birds. Roosts, pallets or boards leaned up against walls or up on concrete blocks, old chairs tables, branches, logs, stumps out in the run can
really help. Lots of diversion and places to 'hide' instead of bare wide open run.
Adding a single bird can be even trickier, best to avoid it, but this might help if it is unavoidable:
https://www.backyardchickens.com/articles/introducing-a-single-hen-to-an-existing-flock.71997/