Does having more apps or tabs open affect battery performance even if they are not being actively used?

Apps and tabs will definitely use power in the background unless they are closed, so it's probably best to close whatever you don't need.

Hi, they don't affect the battery's health, but they do affect the performance. It's like having twenty software opened on a mac's dock, and the mac only has 8Gb RAM--it's going to be slow. And therefore, if you opened ten or more applications you would notice the phone become hotter or the processing speed slowing down. The best thing you can do is restart your phone to free up all of the caches.