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?
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.
Disclaimer: I'm not a lawyer, so I can't take responsbility, yadda yadda yadda.
No. 'Changing' a work 'a bit to make it mine' is a so-called derivative work, for which the original author explicitly owns the copyright.
Besides, taking someone else's work, changing it a bit, and presenting it as completely your own, wouldn't that be deception or fraud, or piracy at the least? Making an image for a tutorial takes way more skills than just the steps described in that tutorial. By presenting the work as your own, you present false proof of having those skills.
Lastly, wouldn't it be extremly ungrateful to the tutorial maker who just taught you a few new skills? More or less stealing their work as thanks?
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.