magic; In two months, I doubt that it would be the rust that caused the pump failure; And, there's nothing you could have done to cause it. Just happens. There is a seal inside the pump that fails. And, there are varying qualities of replacement pumps. Don't know where you purchased yours, but try and stay with a good quality pump. Even they 'can' go bad, but less likely.
Not sure what a 'needle' wrench is?
As far as flushing goes; If you remove the thermostat, this procedure will be quicker; I'd do it before replacing the pump, if you can do it without overheating. Most parts stores sell flush chemicals. Drain the coolant out of the radiator (if still clean, you can save and reuse it; If not, dispose of it properly) and refill with water. Run the engine until warm, then drain and fill again. You can't do this too many times. Each time, it'll get a bit cleaner. Once you are 'satisfied' with the results, refill again with water, add the flush chemical, and do it again following the instructions on the chemical container. This stuff will be, more than likely, toxic, so when you drain it out, dispose of it properly. I would suggest doing one last clean water flush afterwards to make sure you've got all of the chemical out of the system. A 50/50 mix with water and anti-freeze is ideal. Too much anti-freeze can cause an over heating condition as it doesn't dissapate the heat as well as water. Too little anti-freeze doesn't give you enough freeze protection, rust protection, and boil temp. protection.
Freeze plugs, or soft plugs, really aren't what they say they are. I used to think that they were there in case the water in the engine block froze, they'd allow for the expansion and be 'pushed' out, saving the block. Although I have actually seen this, that isn't what they were designed for. Usually, there are three on each side of the engine block, one or two at the rear of the engine (have to pull the engine or transmission to see them) and usually one at each end of each cylinder head. Replacing the plugs isn't a tough job once you've gained access. THAT (gaining access) can be a nightmare. On your application, it would probably be easier to remove the engine and replace all of them. If it comes to that.