Can I get very high current (1000s of amps) using multi stage op amps

For a linear supply i would recommend using a foldback current limiting scheme, especially on something that has a tendency to be shorted/over driven as often as a bench supply. Theres lots of ways to do this and how you do it will be based on the linear regulator design. That being said googling for 'foldback current limiting' especially on google books should give you all the information you need.

For current measurement, you can go high side or low side, whatever you want. The reason to avoid low side is generally to avoid increasing resistance to ground. The small sense resistor you use probably wouldn't matter much in a bench supply. The easiest way to implement this is to use a custom made IC. Such as the MAX4173 there are lots of manufacturers for these though, look around for the one that best fits your needs/cost/package. There are also some that output PWM which can be more accurate to work with than the ADC on most cheap microcontrollers. You just measure the pulse width using a timer and usually either a pin with external interrupt or a comparator input.

As I mentioned in my comment, your question is too broad for this format. However, in the interest of moving you forward in your project, I propose the question of: "What kind of power supply should I be thinking of building for this use case?"

A lab power supply is generally of the linear variety (as opposed to a switching power supply). I think the first decision here is whether a linear supply will be feasible for you.

That question comes down immediately to the question of heat dissipation. A linear power supply reduces its output voltage by dissipating the excess energy as heat. Worst case for the specs you mention would be 50A at short circuit, although 50A at 1V would be almost as severe. If your unregulated supply (transformer + rectifier + bulk capacitor) output say 15V, the worst case heat dissipation would be \$15V \times 50A = 750W\$. That's one heck of a big heatsink, even with a noisy set of cooling fans.

So I'd be inclined in your position to strongly consider a switching power supply which would vastly reduce the amount of heat dissipation required.

For that I think you'll need to elaborate your statement of your requirements and perhaps then ask a more specific question addressing the next step for you.