Question: I am wondering if it's possible to have works from Photoshop or Illustrator made from online tutorials, into your portfolio? If some work's design can be changed a bit, can it be counted like mine?

Answer: 
You can put tutorial work in your portfolio provided you explain that it is tutorial work. Alas, I don't know if that would gain you much in an interview. The fact that you can finish a tutorial doesn't necessarily translate into design and problem solving skills which is what the person looking at your portfolio wants to see.
I think following the tutorials is good for practice, but either start off with something unique or make the result unique in some way to set it apart, as GoofyMonkey says.

But rather than hiding the fact that your works are tutorial-based, which could be considered deceit and grounds for disqualification (from jobs, contests, etc.), I suggest you address the tutorial works directly, explaining why you included them and what you gained. It's professional, sincere, and shows a commitment to improvement. Just remember to finish with something marvelous, like your best work. Keep in mind that if you don't emphasize the tutorials then, at least as far as jobs and competitions go, they might as well not be there.

For your second question, following a tutorial like "balance your color scheme" with your own image is safe. Following a tutorial like "make a barcode" is questionable. Changing a work's design, however, would be a derivative work that could become plagiarism if you're not careful. I suggest getting the author's permission to be safe.