Hello,
Providing incentives is definitely the best way to encourage customers to leave a review. While also making the process easier helps you to increase the chances. I've used https://apps.shopify.com/product-reviews-addon for this purpose, the in-email review form made it convenient for my customers. Thereby increasing review by almost 300% for me. Comes with upwelling features, and customizable to fit my branding.
for external reviews, we imported them via csv using the Shopify's Product Reviews app, just include the real customer's name, email and review message will be good. If you don't have the email address if it's hidden by the eccommerce platform, then just replace with yours. The emails aren't displayed in the website therefore it won't be penalized.