Hi Blagadán,
...Just a handy tip, if you get a pinhole sized leak anywhere in the cooling system, tip a teaspoon of fine ground white or black pepper in the filler neck and add any extra water you may need, it will block the hole long enough for you to get home and fix it, and it readily comes out with a back flush of the cooling system. I usually have a sealed bag of it in my kit when I go out, just incase, and it has worked everytime for me. Loose tea leaves works for larger holes, but it is harder to get out later.
Sorry to hear about the radiator, but those holes should be easy to fix, they'd just need a bit of brass brazing rod, I'd also suggest while your mate has the brazing gear handy, that you or him push on the other dimples while you are there, just to make sure they don't let go in the future, or either that, do a pressure test on the radiator to bring out any more potential holes.
A good radiator specialist should know how and what to do to do a pressure test.
If you wish to back flush the motor to flush out any junk, I'd suggest you pop out the thermostat first, as the closed cool/cold thermostat will block the flow, before placing your garden hose into a top radiator hose the flow should be the same as the amount going in, a strong gush of water. the same applies to a radiator back flush.
And to check the thermostat, place the thermostat on something to stop it from touching the base of the saucepan and fill the saucepan with cold water until it's level with the blocking plate and place the saucepan on a stove element to heat the water to boiling point, just as the water reaches boiling point, the centre of the thermostat should open, if it does, it's working properly, if not it's stuffed and it will need replacing. The normal opening temp of a working thermostat should be 80c - 84c (176F - 183F), if you find this is too high (which is usually the case in Australia, especially in summer), lower opening thermostats are very readily available.
If you ever replace the thermostat, I'd advise you to drill a small hole, approx. 3mm, in the blocking plate, close to the centre opening, as this will allow the coolant to still flow a tiny bit, but it allows the pressure and temperture to equalise quicker between the colder radiator coolant and hotter internal parts of the engine on very cold mornings, but primarily, it's designed, just incase of the unlikely event, that the thermostat decides to seize or fail, it will take a bit longer for the coolant to overheat due to a blocked or seized thermostat.
Also check that the gaps are clear of obstuctions (i.e dirt, etc) between the fins in the radiator, especially on the bottom, I found that the lower half of my radiator, was full of hardened, road grime when I bought her and it took me nearly 8 hours to clear them individually with a cut-down hacksaw blade.
I conjunction with the anti-freeze / anti-boil / glycol based, coolant, (the good book says 43% concentrated coolant, not pre-mixed and it must be aluminimum alloy friendly, as not all of them are) I'd also put in about 100ml of water soluble oil, as this will help lubricate the water pump shaft bronze bearing and help to inhibit corrosion with the aluminium/magnesium alloy used in the engine, etc.
I know this also may sound strange, but also use demineralised water when you refill the radiator with coolant concentrate, as chlorine, alum and most airbourne pollutants (dissolved sulphur dioxide, etc) that are dissolved in tap water will react with the magnesium in the alloy, therefore enhancing the electrolysis / corrosion effect and increasing the amount of rubbish floating around potentially blocking water galley's, thermostats and other things within the internal cooling system of the engine and radiator.
I use to have cooling issues with my coolant temp sensor not cutting in the thermofan until it was too late and it would vent coolant on to the deck, so I bridged the temp sensor relay with an aftermarket engine run/kill switch, between the common power in and the relay switching power out, to manually switch on the thermofan, especially if I was idling through slow traffic, and cool down the coolant before it overheated. If you can feel with your legs the motor is getting a bit too warm and there isn't enough airflow through the radiator, you just pop the thermofan on, at your discretion and the problem is solved, simply.
BTW, in Australia, they have just started making radiator caps (0.9 sized to fit the ZL) with a built-in temp gauge, which would solve the problem of no temp gauge, the only problem is, where the radiator cap goes on a ZL, you can't see the top of the cap as you are riding, I'd love to get one, but I just won't be able to see it, as the petrol/gas tank is in the way, so it's pointless getting one, but it may work on other bikes that don't have a temp gauge.
...they look like this below.
They can be found at
http://www.cpcauto.com.au/radiator_caps.aspx.
Mick.