FriesBoury

I really admire your motivation and I already noticed that is one of the most important things when you want to create games (or do any other project)

Well, it might be useful to know how the pipeline of developing a game works in the first place.
You can look up some design patterns like Waterfall and Scrum and read what others say about these topics.

Although it's hard to manage the planning of a group of promgrammers without knowing much about programming yourself and you don't know how long it will take for them to program a certain feature. Therefore you might have difficulties noticing when some of the employees are slacking.

But anyhow, I hope you keep up that motivation and manage to keep the people you are planning to direct motivated as well

I'm not sure how it works in the environment you are programming in, but almost always, an image gets drawn beginning from the top left corner.
Therefore the first transformation you do, will use this corner as an "anchorpoint".

Before you do the rotation, try to move your image so the center of your image matches the (0,0) coordinates. Not the top left corner.

so your transformations should be:
- 1: translation with offset(-imageWidth/2, -imageHeight/2)
- 2 and 3: rotation and scale (both don't affect position of anchorpoint, so order doesn't really matter here)
- 4: translation to match image center with frame center (frameWidth/2, frameHeight/2)

I hope this was useful to you.

It's indeed a good idea to start by using Unity3D.
I have good experience with this engine myself. It's especially good for prototyping and there are lots of good tutorials on the web on how to program certain features.
It's even possible to make 2D games in it, although the engine is written specificly to support 3D so that might be a bit tricky...

For 2D games I could also recommend Adobe Flash. I'm sure the web is full with tutorials on that

Before you actually start designing a game yourself(storyline, artstyle,...) try experimenting with some game mechanics.
Just for example make a rectangle jump around in a simple platform level. When that feels right, start adding other gameplay features like interaction with the level (levers, buttons, doors,elevators,...) or even add enemies.
Once you made a simple prototype, you can build your story / artstyle around that.
This way you won't get stuck on mechanics you planned to have in it, but didn't manage to write in code yet.

Also important for a self-educating programmer: Use search engines like Google a lot! don't let something you don't know how to do hold you back but search for help on the internet, because there are lots of people coming across the same difficulties as you.