Why is the arrow not rendering to the right

You can use config.rightside and add it to the coordinates of the right line's ends.

However, I did see that config.rightside didn't exactly sit at the end of the frame, like you said. So with framewidth of 8.0, I added around 3 to the coords.

config.frameheight = 14.222222222222221
config.framewidth = 8.0
config.framesize = (1080,1920)

And wrote something like:

self.add(Line([0, 1, 0], [0, -1, 0]))
self.play(Create(Line( config.rightside + [2.8,1,0], config.rightside + [2.8,-1,0] )))

You can similarly add this to the end coordinate of the arrow like:

self.play(Create(Arrow([-1, -1, 0], config.rightside + [3, 1, 0], 
 color=ManimColor('#00FF00'), 
 maxtiplengthtolengthratio=.1), run_time=.5))

You can play around with these values and get want you want to show, I guess. This is a hardcoded solution.

Here's what this looks like:

bluearrow = Arrow([-1, -.71, 0], [1, .37, 0], color=BLUE, maxtiplengthtolengthratio=.1)
self.add(bluearrow)
rotate around its start point (pivot)
self.play(bluearrow.animate.rotate(PI/6, aboutpoint=bluearrow.getstart()), runtime=0.6)

from manim import *
class S(Scene):
    def construct(self):
        start = np.array([-1, -.71, 0])
        target = Dot([.9, .32, 0], color=BLUE)
        theta = ValueTracker(0)
        bluearrow = alwaysredraw(lambda:
            Arrow(
                start,
                start + rotatevector(np.array([2.0, 1.08, 0]), theta.getvalue()),
                color=BLUE,
                maxtiplengthtolengthratio=0.1
            )
        )
        self.add(target, bluearrow)
        self.play(theta.animate.setvalue(PI/4), runtime=1.0)