Submit Redirected URLs When Changing URLs
It makes sense to submit both the old and new URLs when you have changed them. Google may increase the crawl rate automatically when it thinks something has changed.
Don’t Deliberately Block Pop-ups for Googlebot
If you have a pop-up which doesn’t show in Fetch and Render, then it probably isn’t seen by Googlebot. But if you are using a technique to block this deliberately then it could be interpreted as cloaking and result in a manual penalty in extreme situations. If Googlebot is able to see the pop-up, it might result in the content on the pop-up being given more weight than the content on the page.
Lazy Loaded Images Won’t Be Indexed
Images loaded via lazy load probably won’t get indexed, particularly if they are not showing up in the Fetch and Render tool.
AJAX is not 100% equivalent to normal static HTML pages, but it should be possible to make pages rank as well. Avoid using fragments in URLs, and check with Fetch and Render.
Use Fetch and Render to Test Overlays
If you have some kind of overlay or pop-up on landing pages, you can check what it looks like to Googlebot using the Fetch and Render tool in Search Console, and check the impact on engagement using web analytics.
Fetch & Render Shows Results for a Googlebot and Browser User Agent
The Fetch and Render tool shows you 2 different renders, one for Googlebot which used the Googlebot user agent, and one for users which used a browser user agent. If JS/CSS is disallowed for Googlebot, it may not be able to render all the content in the same way.