I have been suspended, should I include that in my college applications?

You should def disclose your suspension on your application since it's likely that schools will have access to it on your transcript. It might play into how schools will consider you as an applicant, but it doesn't mean that colleges will write you off completely. I would suggest trying to explain the circumstances around the suspension and how you handled the situation. Be sure to take accountability for the mistakes made and whether you were able to grow/improve from it and I think that can go a long way in your application. Best of luck!

I'm pretty sure this question gets asked on the common app and you should say yes. You do get the opportunity to explain the situation and why it happened. Make sure you do that. If you lie and a college finds out they will most likely rescind their offer. It's not worth the risk by any means.

Colleges will see that on your academic transcript, and I would still address it in your essays somewhere to make sure you don't try to hide anything. Might give you a chance to explain why it happened and how you grew as well.