Changing lines to inset axes-CodePudding

I'm using matplotlib v. 3.0.3. I wanted to use inset axes to zoom in on a location in an imshow plot and then plot the zoomed in sections outside the main image. I was playing around with the inset axes using the following code

import matplotlib.pyplot as plt
import numpy as np
#from mpl_toolkits.axes_grid1.inset_locator import (inset_axes, InsetPosition, mark_inset)

fig, ax = plt.subplots(figsize=(6,6))
Z2 = np.random.rand(512, 512)

ax.imshow(Z2, interpolation='gaussian', cmap = 'RdBu', origin='lower')
ax.tick_params(axis='both', bottom=False, top=False, right=False, left=False, labelbottom=False, labelleft=False, labeltop=False, labelright=False)

# inset axes...
axins_1 = ax.inset_axes([0, -1, 1, 1]) # bottom left, outside main plot
axins_1.imshow(Z2, interpolation="gaussian", cmap = 'RdBu', origin='lower')
axins_1.tick_params(axis='both', bottom=False, top=False, right=False, left=False, labelbottom=False, labelleft=False, labeltop=False, labelright=False)
# sub region of the original image
axins_1.set_xlim(100, 150)
axins_1.set_ylim(85, 135)

ax.indicate_inset_zoom(axins_1, edgecolor='0')
#mark_inset(ax, axins_1, loc1=2, loc2=3, fc="none", lw=1, ec='k')

# inset axes...
axins_2 = ax.inset_axes([1, -1, 1, 1]) # bottom right, outside main plot
axins_2.imshow(Z2, interpolation="gaussian", cmap = 'RdBu', origin='lower')
axins_2.tick_params(axis='both', bottom=False, top=False, right=False, left=False, labelbottom=False, labelleft=False, labeltop=False, labelright=False)
# sub region of the original image
axins_2.set_xlim(400, 450)
axins_2.set_ylim(200, 250)

ax.indicate_inset_zoom(axins_2, edgecolor='0')
#mark_inset(ax, axins_2, loc1=2, loc2=3, fc="none", lw=1, ec='k')

# inset axes...
axins_3 = ax.inset_axes([1, 0, 1, 1]) # top right, outside main plot
axins_3.imshow(Z2, interpolation="gaussian", cmap = 'RdBu', origin='lower')
axins_3.tick_params(axis='both', bottom=False, top=False, right=False, left=False, labelbottom=False, labelleft=False, labeltop=False, labelright=False)
# sub region of the original image
axins_3.set_xlim(400, 450)
axins_3.set_ylim(400, 450)

ax.indicate_inset_zoom(axins_3, edgecolor='0')
#mark_inset(ax, axins_3, loc1=2, loc2=3, fc="none", lw=1, ec='k')

plt.show()

Here, the main plot is the top left while the top right and both bottom pictures are the zoomed quantities. This generates almost exactly the plot I am after inside the Jupyter notebook. However, I have two issues that I'm looking to fix.

My first issue is that when I save the plot it comes out as follows

which clearly cuts off the zoomed images. I was wondering how to fix this?

The second issue is that the lines running from the subsections of the main plot to the zoomed images cross over in multiple places. What I would like is to keep the boxes around the subsections but change the lines. However, from