General questions/observations/discussion

Maybe it's a silly question but can you do cycle training riding a brakeless?

Assuming you mean on a fixed? Basically, no. It's illegal to ride one and the trainer would not be insured to ride with you. A trainer might do a private lesson with you though. It's a tricky one really; we all want riders to have training, believe it is better for a rider to have training but cannot be seen to endorse illegal behavior. Part of Level 1 cycle training involves doing an emergency stop. Who knows, the results of that in itself might be enough to convince someone to get at least a front brake.