First of all, can you confirm that understanding is correct or have I got this absolutely wrong?
Not absolutely wrong but a bit naive. The current you can get out of the battery has nothing to do with the batteries capacity, it is a totally different thing. A 2000mA / hour source will not deliver that in a usable form you are better off halving that for any practical purpose. That capacity will quickly go down as you use the battery.
As you use a battery, does the voltage remain constant
No the voltage drops slightly until it is nearly exhausted then drops rapidly.
does that mean it will be 0.75V or will the voltage remain the same
No not any of that, the voltage drop with dropping capacity is different on different types of battery, any attempt to guess the remaining capacity based on the voltage is a bit hit and miss as you will know if you have ever used a laptop.