Would I get to download the game again after the reset?
Yes, you would. You can redownload the game from the "Library" tab on Google Play (or, since Minecraft hasn't been unlisted, just search for the app again in the store; it should show you "Download" instead of the app's price in the green button). Keep in mind you have to be logged in with the same account that originally bought the game.
Would it save my worlds?
I sadly couldn't really find any definitive answer to this (I can't speak from experience since I never played the PE outside of the demo). However, if the Bedrock edition on Windows 10 is anything to go by: yes, it would.
I would still recommend backing up your worlds just in case, which brings us to
How can I save my worlds just in case?
I found this tutorial about how to backup your worlds in both the Android and iOS versions. The steps are as follow:
Stop the Minecraft app before creating a backup.
Open the "My Files" application and open the >games>com.mojang>minecraftWorlds-folder. Each folder on this location contains one Minecraft World.
From there, copy the worlds you want to keep to an external storage (in this case, a microSD), and then paste them inside games>com.mojang>minecraftWorlds after the factory reset.