The app will not leave any code once removed/uninstalled. Sticky Add to Cart Booster Pro does not alter your theme in any way either.
Absolutely. The Sticky Add to Cart button calls the same events as the regular theme's Add to Cart button. The app doesn't add additional Facebook pixels. It will use an existing Facebook pixel if one is configured on your site.
Yes and no. The Sticky Checkout Bar/Button behaves the same as if the regular Checkout button was clicked so that feature is compatible. The Skip to Checkout feature cannot be used with subscriptions. The Quick Buy Button feature doesn't support subscription apps yet. Sticky Cart should link to the cart page, not checkout since subscription apps require that users go to checkout from the cart page.
Any fields that might be required by a personalization app and its data will work properly. The Quick Buy Button feature will NOT show options from the personalization app though. The Skip to Checkout feature cannot be used with these apps.
No, it will not slow down your site. We take this very seriously. The app is fully optimized so that it will not make any impact on your store's page speed. We use best practices such as caching, CDNs, and various code and speed optimizations to avoid this.