iPhone battery issue

Yes, you can use your phone while charging however it will charge faster in not in use.

I have the same issue with my iphoneX running iOS13.

There could be a number of things causing your battery to drain fast.

First i would suggest doing the following -

1. 1. 1. Open "settings" and scroll down to "battery" - this will give you insight to whether this is the device's battery itself or a user/software issue. It will show you which apps are draining your battery.
      2. Swipe up from the bottom of your phone (app switcher) and close all applications not in use
      3. Turn off "background app refresh" unless needed
      4. Turn on "low power mode" and "auto brightness"
      5. Turn off bluetooth and wifi when not using at home

There is no reason why you cannot use your device while it is recharging.

When to charge your iPhone or iPad - Apple Community