I had bought a Sony Xperia Z1 (Snapdragon 800) in 2016. It came with the Android 5 version but it has only 2 GB RAM. So, f I install custom ROM, will it improve my device performance, will it increase the battery life?
Yes. And no.
The hardware is really old now. You can make some tasks lag free with vanilla android, but tbh, sd 800, 2gb ram can’t handle much now a days. And you can improve battery life with the help of greenify by restricting apps, but for gaming, nope.