Kx 125 Rebuild Manual
These answers are based on general know-how, I have never done a top-end on your specific bike: 1. No, unless you consider needle-nose pliers a special tool. No, unless the bike has a ton of hours or has been ridden very hard. Having the bore honed would be ideal, but is optional. I believe there's only one size piston available for your bike (could be wrong).
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1989 Kawasaki Kx 125 Rebuild Kit
Yes, you should inspect it, it's fairly easy to disassemble and re-assemble. I would recommend giving everything a good cleaning and de-carboning. I would recommend purchasing a service manual for your bike before you do your top-end.
This will take you through it step-by-step and also tell you if any special tools are necessary. As a general rule, it doesn't get any easier than a 125 top-end, but if you've never done one before the manual will help. If the cylinder has been scored or otherwise messed up then it will need to be bored out to the next 'oversize' and you will need to get a new piston to match. Measuring the cylinder is not easy and unless you are skilled in the art you probably would not be successful even if you had the right tools, which can be expensive. You can take the cylinder to the machine shop and have them measure it for you. Another way is to buy a new set of rings for your current piston, slip the ring into the cylinder (not on the piston, just the ring) and measure the end gap. If the gap is larger than the specification then you need to bore out to the next size or replate (if your cylinder is the type that is plated).