You can find most anwers in the datasheet of the L298.
Do you want to use the L298 as a component, a breakout board is easier: https://www.sparkfun.com/products/9670
1) The motors require 1A ? You have to know the maximum current, that is called the "stall current". Once you know that, you can choose the right driver. Can you post a link to the motors please ?
2) You can use the 1N4007. The 1N4007 is for a higher voltage, but they are the same as the 1N4001.
3) According to the datasheet:
pin 4 = Vs = Supply Voltage for the Power Output Stages. That is the power supply for the motors.
pin 9 = Vss = Supply Voltage for the Logic Blocks. That is the Vcc, the 5V of the Arduino.
4) According to the datasheet: "Between this pin and ground is connected the sense resistor to
control the current of the load
5) The 'normal' L298N has a heatsink.
The question is: should you use the L298 ?
I think not.
At 1A, the voltage drop of the L298 is 1.35 and 1.2V (read the datasheet). So the motors get 5V - 1.35 - 1.2 = 2.45V ! That is way too low.
So lets drop the L298 and use a mosfet driver. Power mosfets have only little voltage drop.
Sparkfun has a nice selection: https://www.sparkfun.com/categories/179
But there are many more.
You have to know the stall current, and the mosfet driver should be capable to operate at 5V motor voltage.