I'm applying for Parsons (interior design) School. Does the portfolio have to include everything Interior design related or is it okay if I include some of my sketches and art which are not Interior design related?
You can and should include sketches and other things. Parsons isn't looking for Interior Designers, that's what they'll be teaching you. They're looking to see if you have a genuine interest in design and any sense of the fundamentals: balance, color theory, shape, scale, etc.
If a program wants something specific than they generally will have some sort of additional criteria or clearly stated things to include in the portfolio. The Cooper Union for example has a home test they include as part of the application which is separate from Portfolio.
Having said that I also want to let you know that Interior Design is a very tough degree and Parsons isn't an accredited school. You might want to consider others instead.
I'd have to agree with what's been said -- no one expects you to already be an interior designer. So a strong portfolio full of that isn't required, naturally. Though if you have sketches for things, I wouldn't hesitate to include them.
Include your best work even if you don't think it's great. I remember applying to School of Visual Arts for Graphic Design with horrendous drawings in my portfolio...Here's the kicker though. I showed passion and motivation. I ensured that they knew I was working very hard to get better. In fact, showing a progression if you can is also extremely helpful.
Be sure to include any honors, activities, good grades, etc. That's always required for college...But at the end of the day the story I think one should be telling for college is how you're hard working and need that particular school to help you improve. How it will make you even strong and that you are capable.
Also, Parsons is great, but don't forget to apply to multiple schools. I also recommend checking out FIT and SVA.