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: 
My suggestion would be to do the tutorial using the files and steps they give you, then use the techniques you've learned to create something that is your own. It will show much better in your portfolio and it might not be as easy to recognize as a tutorial.

Most of the creative people who are going to review your portfolio for a job are probably poking around the design sites, and reading the magazines you got the tutorial from anyway. So, if you just include the tutorial files in your portfolio, they will probably recognize it pretty quickly.

Added bonus: Doing it again will also help you learn the technique better and help cement it in your brain to pull out later when a job will call for it.
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.