Glyphosate is the chemical involved in the weedkiller. Roundup is the best-known trade name but you can get others e.g. Resolva (this has a second chemical so you can see within 24 hours where you've missed bits ... ) or an unbranded version.
It comes in pre-mixed versions and in concentrated ones, as you say. I'd always go for the concentrated one - it goes further and lasts longer (though more expensive up front). The dilution rates will be on the packet for spray or watering on (use a dedicated watering can, perhaps of a red colour, so you don't reuse it for watering your prize roses next year by accident ...
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Don't apply it in windy weather because of the risk of spraying other plants, and don't apply it if the weeds are wet or rain is forecast in the next 6 hours.
At this time of year the plants won't be growing that actively, so I'd leave the weedkiller to do its business for 10-14 days before starting to attack it if you can. No need to test the soil.
I need to do this with my own lawn but the weather is currently defeating me ...