It would be incorrect to assign ق ء ل as the root of قَائِلٌ. The root is ق و ل, revealed by قَوْلٌ and يَقُولُ.
بَائِعٌ contains hamzah, but its verbal noun بَيْعٌ and imperfect يَبِيعُ show an original yāʾ.
خَائِفٌ comes from خ و ف, with wāw visible in خَوْفٌ.
Comparing the perfect, imperfect, verbal noun and participles is more reliable than inferring radicals from one surface derivative.
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Recovering Roots from Derived Forms
Hollow Verbs: Seven Iʿlāl Rules and Three Short Paradigms
It would be incorrect to assign ق ء ل as the root of قَائِلٌ. The root is ق و ل, revealed by قَوْلٌ and يَقُولُ.
بَائِعٌ contains hamzah, but its verbal noun بَيْعٌ and imperfect يَبِيعُ show an original yāʾ.
خَائِفٌ comes from خ و ف, with wāw visible in خَوْفٌ.
Comparing the perfect, imperfect, verbal noun and participles is more reliable than inferring radicals from one surface derivative.