I have noticed with some European pilots, especially those from Scandinavian countries, will ask you to confirm that they are cleared for the ILS after you have given them a closing heading to establish on the localiser. Perhaps over there they need approval in the form of "cleared for ILS approach runway xx".
With regard to the first message, there are sometimes circumstances when we want the aircraft to establish on the LLZ but NOT to descend (as a way of guaranteeing separation against slower and lower traffic ie at 2A) - but perhaps my unit does that more than some others...
In formal RT phraseologoy "descend on the glide", "continue with the glide", "continue with the ILS" do not exist, and should not be used. If pilots want to read those phrases back then that's up to them. Nothing more embarassing than getting an RT transcript and READING your own cr*p RT phraseology..
And when I'm busy I stick with "Descend ILS" - quick as "continue approach"
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Foo Man Chew