A. Anytime you need electrical work done it may cost more and could be dangerous if an unqualified person attempts to do it.
A. Any time you get new equipment that requires too much power for existing circuit most appliances and heaters require a dedicated circuit.
A. Call an Electrician it may not be overloading, it could be a fault in the circuit or breaker that may need replacing if it repeatedly trips.
A. Call an electrician to add an additional outlet
A. Yes, the bulbs in the fixture will have to be dimmable.
A. Could be wired incorrectly, or need to be replaced. This also could be a ground fault on equipment plugged into the circuit or somewhere on the circuit itself.
A. If a cord is plugged into it and it wiggles easily should be a tight fit also if there is black marks. Outlets in bathrooms and kitchen over countertops or near sinks need to gfci receptacles or protected by gfci. Also outdoor outlets/receptacles and in garages needs to be gfci protected