Travel
You can travel once supervision ends. Canada is the one that catches people, and it catches them at the airport.
Permission first
Leaving your district needs permission. Leaving the country needs more than permission and often gets denied.
After supervision ends, you can travel. Other countries are a different story.
Canada
Canada treats a criminal record as grounds to refuse entry, and they see your record at the border.
You can become admissible again. There are three routes: automatically, after enough time has passed for a single lesser offense; by applying for criminal rehabilitation; or by getting a temporary permit for one trip.
All of it takes paperwork and lead time.
Mexico and Europe
Mostly less trouble. Some countries ask, some don't, and rules change.
Global Entry and TSA PreCheck
Both are usually denied with a felony conviction, though it depends on the offense and how long ago.
Check before you book
Every time, for the first several years.
Getting a passport is a separate question and mostly a simpler one. That is in Your rights, and when you get them back.
Kids, community, and dating
Coaching, chaperoning, scouts. Almost all of it runs a background check. And you have to tell the people you date.
These pages cover the general rules. Your situation has details they don't. Email me a question. Answers are free, and "you don't need to pay anyone for this" is my most common answer.
I answer in the order received, usually within a couple of days. I have a day job. If your situation genuinely needs more than an email, I take a limited number of consults, so say so and we'll work it out.
Somebody else is two years out and stuck on the same thing. Pass it on.