Why is tirer in the infinituve form here please, rather than "shooting" or "they heard that someone had shot"?
Because it follows another verb - entendre - conjugated in the passé composé. Whenever one verb follows another in a single statement (ie without a conjunction) the first may be conjugated but the second (and subsequent) verbs must stay in the infinitive.
Why does the entendre verb not agree with the ils?
This lesson is concerning me with all the death and shooting
Then the evening news and the daily newspapers should disturb you greatly!