Yes. That trailer has a GVW well in excess of 10,000 lbs... it's probably closer to 16 or 20k... and the F350 has a GVW of 13,000 lbs. That combination requires a Class A CDL.
That's the class of licence you're required to have in order to drive an 18 wheeler...
If you already have a CDL, you take the written air brakes test, then do a road test in a vehicle of the appropriate class which is equipped with air brakes.
No, you cannot. Canada is part of the ICC, and shares commercial driver information with the American FMCSA. If you try obtaining a US licence while possessing a Canadian one, or vice versa, they'll find out about it. By the way, "CDL" is a term exclusive to the US.. Canada uses a different system. Class 1 is the equivalent to a Class A CDL, Class 2 is equivalent to a Class B, and I believe Class 3 is for buses and such.
It will vary depending on the specifics of the job, the company, and how much experience the driver has. Not all Class 1/2/3/etc. jobs (Canada does not have the CDL) are going to be the same.
Class B CDL, and you can't have an "L" restriction (L restriction indicates you're not permitted to drive vehicles with air brakes). If you're expected to tow a trailer behind that dump truck which has a gross weight of over 10,000 lbs., then you'll be required to have a Class A CDL, again without an "L" restriction.
You probably can't get a CDL with one DUI, let alone three. But you need to check with your licensing agency, you may need to just pay extra or wait until the DUIs drop off your record.
You can get the CDL. Good luck finding a job where you get to use it, though.
I wish... I paid $318 in 2010 to renew my Class A CDL at $15/year (8 year license) with three endorsements at $3/year each, plus $96 for TSA fingerprinting and a background check for my hazmat endorsement. And those prices reflect the cost of a CDL. For non-CDL licenses (of any class), it's $4/year (again, typically an 8 year license), and an additional $1.75/year if you're getting a motorcycle endorsement.
I'm not sure on how it works in the United States, but in Canada you need what is called a Class 1 Licence, which allows you to drive pretty much anything. You can drive just a tractor with a Class 3 Licence with an air endorsement. In the US, you can drive just the power unit with a Class B CDL, and you need a Class A CDL to drive the whole combination. Your licence must not have the "no air brakes" or "no tractor-trailers" restrictions on them.
I'm assuming you mean "over the road" by OTR. If you plan on doing. it in a tractor trailer or expedited van with a gross weight rating of over 26,000 lbs., then yes. You can still drive OTR without being in a vehicle requiring a CDL, however - companies like Tri State, Fed Ex Custom Critical, Panther II, etc will lease out owner/operators with a 3/4 ton or 1 ton cargo van, although you would need a Class C CDL with hazmat endorsement if these companies required you to have hazmat on your licence.
You need to get a lawyer.