Hi Nelson,
Thank you for sharing the admin access.
For step 1, you can create a new taxonomy view, that can create a custom form, where each term in the "Network Sites Categories" taxonomy is a checkbox, and value is set to use the term ID.
( please refer to the view named "View to generate Network Sites Category checkboxes" and the page named "Page 1" )
Example content from the "Loop Editor":
[wpv-layout-start]
[wpv-items-found]
<form action="[wpv-post-url item='4018']" method="get">
<div class="form-group">
<label for="wpv-network-sites-category">Network Sites Categories</label>
<!-- wpv-loop-start -->
<wpv-loop>
<div class="checkbox">
<label for="network-sites-category-[wpv-taxonomy-slug]">
<input type="checkbox" id="network-sites-category-[wpv-taxonomy-slug]" class="js-wpv-filter-trigger" name="wpv-network-sites-category[]" value="[wpv-taxonomy-id]">
[wpv-taxonomy-title]
</label>
</div>
</wpv-loop>
<!-- wpv-loop-end -->
</div>
<input type="button" class="wpv-reset-trigger js-wpv-reset-trigger" name="wpv_filter_reset" value="Clear">
<input type="submit" class="wpv-submit-trigger js-wpv-submit-trigger btn btn-secondary" name="wpv_filter_submit" value="VIEW SELECTED CATEGORIES">
</form>
[/wpv-items-found]
[wpv-no-items-found]
<strong>[wpml-string context="wpv-views"]No items found[/wpml-string]</strong>
[/wpv-no-items-found]
[wpv-layout-end]
Please note how this custom form is set to submit to the same page's URL with ID "4018".
Important: this website is set to use the "Plain" permalink structure where each page's ID is appended in URL parameter, but for this custom form to work, you'll need to change that to a different permalink structure that uses page slugs.
( ref: https://wordpress.org/support/article/using-permalinks/ )
The next step would be to show the view "Network Sites Categories" that you have already created, below this custom form, but only once this form has been submitted.
For this part you can wrap that view's shortcode inside a conditional block, that checks whether the URL parameter "wpv-network-sites-category" is set or not:
( https://toolset.com/documentation/user-guides/views/conditional-html-output-in-views/using-shortcodes-in-conditions/ )
[wpv-conditional if="( '[wpv-search-term param='wpv-network-sites-category']' ne '' )"]
[wpv-view name="network-sites-categories"]
[/wpv-conditional]
As a result, when a visitor will submit the form on "Page 1" the IDs of the selected term IDs would be passed in the URL parameter on the same page, and when the page will refresh, only the results from the selected categories will show below.
I hope this helps and please let me know if you need any further assistance around this.
regards,
Waqar