Is it legal for a broker of insurance to cancel your policy if they do not send you the warning-letter from the insurance company and they put things on your insurance policy that you never asked for?
There are two separate questions here, cancellation and adding stuff. As for cancellation, you have to look at the applicable laws. In Washington state, for example, there is a law governing insurer cancellation of insurance. For insurance other than fire and medical malpractice insurance,
The insurer must deliver or mail written notice of cancellation to the named insured at least forty-five days before the effective date of the cancellation
and for medical malpractice, the timing is 90 days; or 5 days for fire insurance. The net result is that all forms of insurance require written notice of cancellation.
The terms of an insurance policy can be changed by the insurer: they must tell you of these changes, and you do not have to "ask for" them. If you don't like the changes, you can attempt to persuade them to not make the change, or you can cancel the insurance.
Whether or not an insurance broker is authorized by the insurer to act in a particular way depends on the broker's actual relationship to the insurer. In Washington state, agents and brokers are subsumed under one concept "insurance provider". Agents and brokers are generally not empowered by the insurer to do wholesale re-writings of policies (e.g. adding coverage for seismic damage for all customers). An agent or broker cannot, however, unilaterally add "medical malpractice insurance" specific to your homeowner's policy without your approval.
It depends who’s agent the broker is
If it is a general insurance policy (property, motor, liability etc) then the broker is your agent. A notice delivered to them is legally a notice delivered to you.
If it is a life policy (life, income protection, TPD etc) then the broker is the insurer’s agent. A notice delivered to them is just the insurer talking to themselves.
This is the common law default for historical reasons, however, specific jurisdictions may have other rules.