The elementary logo comes from the plymouth. Plymouth has different themes and it looks like you have changed the theme. In order to return to the elementary theme you have to type into terminal
sudo update-alternatives --config default.plymouth
and type the number of the /usr/share/plymouth/themes/elementary/elementary.plymouth theme in your list.
I believe this is the same issue I had, but you don't use disk encryption so you just see a black screen shortly on boot and then are greeted by the login manager.
See here for my solution: Black screen instead of plymouth
(Sorry, I can't post this as a comment because I don't have enough reputation)
UberWriter does not support Ubuntu 16.04 (upon which elementary is based), thus the command to add the PPA fails.
You may however install it from source with the following:
Install pre-requisite packages: sudo apt install build-essential
Grab the code: bzr branch lp:uberwriter
From inside the project directory, install UberWriter with sudo python setup.py ...