I think it's best to start by explaining, for any users who may not know, what diabetes is and what insulin does.
Insulin is a hormone, produced in the pancreas, that allows the body to regulate its blood sugar levels. In type 1 diabetes, the pancreas stops producing insulin; type 1 diabetics thus have to inject themselves with insulin at regular intervals, or else their blood sugar will climb to dangerous levels. In type 2 diabetes, the body becomes resistant to insulin, often - but not always - as a result of obesity or lack of exercise. Type 2 diabetes can be managed by exercising, eating healthily, and if necessary, medication.
With that out of the way:
- is it possible to have diabetes (even some easier type) and compete on the world level in strongman (or similar) competitions? (Especially with a diabetes unfriendly diet.)
Absolutely. Sir Steve Redgrave was diagnosed with type 2 diabetes in 1997, and it didn't stop him from winning his fifth Olympic gold medal at the Sydney Games three years later. Spanish footballer Nacho was diagnosed with type 1 diabetes at age 12, but has still carved out a successful career with Real Madrid. Wikipedia has an entire list of diabetic athletes, though it also includes athletes who developed type 2 after they retired.
As for "diabetes unfriendly diet" - bear in mind that athletes, especially strongmen, have different dietary requirements to most people. They perform more exercise, and more strenuous exercise, than most people, therefore they require more calories - and since exercise uses up your blood sugar, they need more blood sugar too. So while that strongman's diet may well be unhealthy for an ordinary person, it almost certainly fulfils their own personal requirements.
Additionally, type 1 diabetics can simply adjust their insulin dosage to account for any sugary foods they may eat. With careful management, there is no such thing as an "unhealthy diet" for a type 1 diabetic, and they can basically eat whatever they want as long as they account for it. (I don't think this is the case for type 2 diabetes, though.)
- is it legal to use/abuse insulin with an official diagnosis of diabetes - if so, why all athletes do not have diabetes formally?
I initially wasn't sure how one could "abuse" insulin. Certainly it would be a dangerous game: injecting too much insulin results in hypoglycemia, which at best makes you lethargic and clumsy (not desirable traits for an athlete), and at worst is fatal (see the film Memento).
In the comments, you linked to this paper, which describes how insulin is in fact abused as an anabolic steroid. However, the same paper notes:
[T]here is a paucity of data on the use of insulin as a PED [...] there is no evidence of improved muscle mass after insulin administration in healthy adults at this time.
So while some people do abuse insulin to try and gain an advantage, there doesn't seem to be any evidence that it actually works. (In any case, the paper also states that the IOC have banned non-diabetic athletes from using insulin since 1998.)
Even if there were an advantage to be gained from having diabetes, its two main causes are genetics (which are something you have no control over) and obesity/lack of exercise (which, again, are not desirable traits for an athlete). So an athlete trying to give themselves diabetes on purpose would find it very difficult - and would probably become uncompetitive through lack of fitness long before any benefits of type 2 diabetes kicked in.