I'm a self-taught (C++ and C# Programmer/Software Engineer) who's looking to get into the gaming business, i heard that in order to get there(without any type of degrees) I need a portfolio.
So recently I've been working on building my own Game Engine, that will serve the purpose of being my portfolio and at the same time as a Game Engine that will be used to develop some indie games.
Anyway the engine will be a multi-platform one which will support the Android, Windows and Linux OSes.
And i'm thinking after i finish my engine of developing a game off of it, it'll be a Breakout like game, that is a small game that will show what this engine can do.
So the Breakout game will have some graphics and I'm thinking of selling it on Google Play Store and...(others).

1. Will that approach actually work and get me into the industry?

2. How can i sell my games?
do i need to create some kind of trademark or something(sorry this question might be stupid, i really don't have any idea about the legal side of the business)?

1. Nobody can foretell the future. Your plan might get you into the industry, whether or not you sell your game once you make it. (The portfolio doesn't need to include "and I self-published my game too.") And it might not. Depends on how many of the right things you do, and how many of the wrong things you don't do. See FAQs 24 and 27.

2. Please ask business questions in the Business And Law forum. This forum is about getting jobs in the game industry.

So recently I've been working on building my own Game Engine ... after i finish my engine [I'm thinking] of developing a game off of it, it'll be a Breakout like game, that is a small game that will show what this engine can do.

In my experience, these "engines without games" projects do not go well. The list of things that an engine could do is endless, and the list of ways that you could solve any single one of those things is also endless. On the other hand, a particular game, like Breakout, has a very definite list of requirements.

IMHO, you should always build an engine alongside a game, so that you know exactly which things you should build, and you'll be able to concretely compare different approaches to any problem, by actually testing your engine's features in practice, by building a game that uses them at the same time.

I'm also a strong believer in YAGNI, and I've found that if you write some particular feature months in advance, without actually having a need for it yet, then you won't do as good a job of it. With these kinds of game engine projects, the entire project violates YAGNI! I've found that with these kinds of engines, when you finally decide to use them to make a game, you realise that many features don't quite work the way you'd like them to (or are buggy, because they've never been properly tested), and you end up doing a lot of re-work.

Also, a game like Breakout doesn't need a very complex engine. If you go and create a really complex engine and then use it to create Breakout, then both your game and your engine will be over-engineered.

It would be best to keep your engine as simple as possible while making Breakout, or to make a more complex game with an existing engine, or, make your own very complex engine but also make a very complex tech-demo to go with it.

The best course also depends on what kind of programming you want to do.

A breakout-from-scratch project is a decent project to show that you're a competent programmer in general.

A game with lots of particle systems or post-processing effects might show that you've an affinity for graphics programming.

A game with enemies that take cover and flank the player might show you've an affinity for AI programming.

A game with a GUI level editor might show you've an affinity for tools programming.

A game with a professional data-compilation pipeline might show you've an affinity for engine/tools/build-automation programming.

A game with 10000 enemies on screen at once might show you've an affinity for engine optimisation.

etc...

2 - Depends on your country. You likely need to register a business number and do your taxes correctly. Speaking to an accountant would be recommended.

3 - Your English is perfectly fine

I'm more interested in low-level stuff so i don't think that the YAGNI principle applies here.

It always applies

If you don't need something, then building it is a waste of time, and worse, you can't evaluate whether you've done a good job or not.

I publish most of my low-level engine structures as open source, here, (there's a lot) and each of them has only been created in response to a need. They're all used directly or indirectly by the game project that's being developed simultaneously to the engine.

I'm really trying to get into the low-level stuff of the process of a game making, so I don't think using an existing engine will get me there, or will it?

Also, to build a great product you should be familiar with the competition already on the market so you can emulate their strengths and improve on their weaknesses so having used a variety of other engines is always a perk.

My $0.02 is that there are two ways to impress interviewers with your portfolio.

1. Show them something that looks impressive.

2. Show them something that is finished.

If you want something that looks visually impressive then use an existing engine. If you want to get down and dirty in engine code and Unity doesn't scratch that itch for you then look at Torque or Ogre or something.

If you want to get something finished (by which I mean completely finished, polished and available on an appstore or something), then use an existing engine.

The problem with spending your time on your own engine is that even if you do great work in there, it's just not going to be visible and your interviewers are never going to dig around the source code to appreciate the elegance of your file handling or shader uniform management code. And to be honest, you're not going to do great work writing your own engine, you're going to be learning a huge amount, but your code will be a bit of a mess, your second engine will be the good one.

Good luck, whatever you decide.