Week 1:
This week I started by making some basic sprites e.g.:
Player: 
Enemy:
Bullet: 
Then I began to write some scripts for a basic movement system (which should be relatively easy to port to mobile), a basic shooting script (which will eventually be upgraded to a small weapon system) and one script to make the player look at the mouse (where I had a small problem because the player looked in the opposite direction of where the mouse was pointing. This happened because I implemented an offset into the code, but I thought I had to rotate the sprites -90° which was unnecessary. To fix it, I just set the offset to 0°)
For next week I plan to make...
...a script to spawn the enemies.
...a script for player health and hook it up to a health bar.
and last but not least...
...one to make the enemies follow the player and have them be able to deal damage to him.