a) they are playing a kite (no preposition) c) He hailed the taxi or he was hailing the taxi (no preposition and mind the tense you want to use) All the rest seem to be ok.
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Vincent TeoCan I say,
(a) They are playing with a kite. OR They are playing with kites
(b) They embraced each other warmly. ok
(c) He [is/was] hailing a taxi.
(d) The bridge is over the river. ok