- Edited
AGI I never had such things before. The OS is pretty stable. You can take a screenshot by holding the Power button a little until a menu pops up.
You flash the ROM first, then immediately Gapps without a Reboot in between.
I'd wipe everything again (without the data partition), then use TWRP's file browser to delete all folders on the data partition, especially "Android", but leave the zips there. Make sure to clean the dalvik cache, too. I will tak a look into TWRP to remember if I skipped a step. And you did download exactly this file: http://download.paranoidandroid.co/roms/oneplus3/pa_oneplus3-7.3.1-RELEASE-20171030-signed.zip ?
Edit: OK I'd do the advanced wipe in which you select everything except for "Internal storage". It seems the standard wipe didn't include the system partition. The go in TWRP' main menu, Advanced - File Manager and delete everything in the /sdcard directory manually, except for your Paranoid Android and Gapps files or other downloaded stuff. Then you should be able to do a proper clean install.