What is going to a therapist like?

Not sure, but there may be online therapy. But due to your age, you would almost certainly need to have parental permission. Therapists usually work in a quiet comfortable office style room. They are supposed to be confidential and for the most part they are. But they are legally required to go to the police if they believe you are a serious danger to someone and they also have a duty to warn anyone whose life you are threatening if they believe you can and will carry out the threat. Some therapists, though not most, will also talk to your parent or parents if they think that is the best thing to do.

Well, I don't have that much experience with therapists (as it just doesn't work for me, for some reason), but as people, they're as a rule very calm, friendly, understanding and attentive. It does depend on the therapist, however most of them work in small-ish office or living-area type rooms, which is supposed to comfort the patient a bit more, I believe.
And of course a therapist can be trusted. It's their job, after all! Therapists usually become who they are out of their wish to help people. It's what they enjoy doing, otherwise listening to the woes of hundreds of patients would just wear them down into a horrible state. I'd definitely trust them, if I were you, however again - it depends on the therapist.

As far as online therapists go, there are a few sites where you can contact them, however it's much more effective to talk to someone face to face. 7cups.com is a site that's been around for quite a while and there are some professional therapists there as well, other than the random, yet still caring people you can talk to.

I do hope that everything works out for you in the end and that you get some help to alleviate this sleeplessness. Best of luck to you!

Therapy is easy and fun if you give into the process. Choose a woman therapist. They are much more compassionate. The selection of a therapist you're comfortable with is just as important as what you discuss.

Just do it. You won't regret it. When I was your age, only "crazy people" went to a therapist. Now everyone goes.

Be an active participant in your therapy, that's key.

You can send me a message. I listen. I don't judge (much).