if a bulb is connected in a circuit, which of the following will make it glow:
convection current from the positive terminal or the flow of electrons from the negative terminal?
Convection current consists of positive or negative charge?
Was it believed that convection current is the flow of positive charge?
It is incorrect to say convection electric current. The only convection phenomena are related to heat transfer.
To clarify the concept of conduction electric current first we start with its history. Static electricity was known from ancient times (about 500 BC) when was discovered the property that different substances change their behavior after being rubbed with textile materials. At about 1750 Benjamin Franklin made his famous experiment with the kite and the key, demonstrating that lightning and static electricity flow were the same thing. A few decades later Volta constructed his first electric pile and this way a new concept in physics emerged: the electric current which was defined as the flow of static electric charges.
Now, when the above definition was postulated, people (physicists) did not know about the existence of electrons (and protons and positive and negative ions). They simply know only the concept of static electrical charge (which could be positive or negative).
Thus, by convention, the positive direction of an electrical current is given by the direction of the flow of positive charges. Therefore, the conduction electrical current always flow from the positive terminal to the negative terminal in any given voltage source.
Today people know that the true charge that flows between terminals in a voltage source is given by the electrons (hence negative charge) and therefore the current consist of the negative charge flow, but the positive sense of the current is opposite to this flow of negative charge (the positive direction of electric current is still from positive terminal to the negative terminal).
These said, it is equivalent to say that a light bulb glows as a result of current flow from positive terminal to the negative one, or to say that the bulb glows as a result of electron flow from the negative terminal (to the positive one).