If the earth's radius was half as large as it currently is but with the same mass, how would the acceleration of gravity at the earth's surface change,and by how much

The acceleration of gravity depends on two things.

One thing is the planet's mass, so that wouldn't cause it to change.

The other thing is the square of your distance from the planet's center.
You said that the distance is reduced to 1/2 of what it used to be, so
that tells us that the acceleration of gravity ... and the weight of every
thing and everybody on Earth ... would increase by 2² = 4 times.

The second Statement The algebraic sum of the currents flowing through each of the three resistors is equal to the current through the battery.  

In a series circuit, the value of the equivalent resistance is equal to the sum of the values of each of them:  

 

Where:  

The equivalent resistance of the combination of resistors is greater than the resistance of any one of three resistors.

In this case the current flowing through the resistors is the same in each one. This is because the current flowing through the circuit only has one way to go, so the current intensity is the same throughout the circuit.

Therefore:  

The current flowing through each of the resistors is the same and is equal to the current through the battery.  The algebraic sum of the voltages across the three resistors is equal to the voltage across the battery.  

The battery provides a voltage that is the sum of the different voltages at the ends of the resistors:  

 

Where the Voltage, according to Ohm's law is:  

 

Hence, the second statement of this question is True