Hello everyone, first post!
I decided that I want to learn how to program (i.e code) with the ultimate goal of making my first 2D game for mobile phones.
As far as my experience goes I know very (very very…) little about programming, but just enough so I won’t get frighten by just looking at a script. I want to start all over again with the basics of code writing and gain full proficiency before moving on to making games. is unity a good place to start?
There are tutorials in the Learn section of this site that start from knowing nothing about programming and teach that. Personally though I would suggest spend a weekend learning the basics of programming on a site like Codecademy and then picking up Unity-specific code will be a breeze. Once you already know the basics of programming you could checkout a resource like my book Unity in Action.
What he said. I would only add: yes, it is not only possible, but a very fun and productive way to learn programming.
Last year I taught a bunch of middle schoolers who had never programmed before how to program in Unity, while developing a spacecraft simulator for the school aeronautics club. It was a blast and they all learned a lot. Just hang in there, ask clear questions, and be patient while you level up your mad skillz!
Just start doing, you will go from Hello World to a 2D game in a few weeks.
I would say that Unity is the best place to start programming if you like games 
I officially begun learning C# and JavaScript in Unity, though I had worked on C++ (just a bit) and VisualScripting (I think it was called that) on Windows Maker, Visual Studio. Unity is a perfect source to learn coding, both structurally and logical programming.