Learn German: Der Täter rannte sofort in den Schatten. - The perpetrator immediately ran into the shadow.

rennen is a mixed verb. Mixed verbs combine features of both weak and strong verbs. They change their main vowel in the past tense (like strong verbs do, here changing from e to a), but they also add the typical weak verb ending -te. That is why the stem renn- becomes rannte.

Would a German speaker actually say rannte in normal conversation, or use the Perfekt tense (ist gerannt)?

While the spoken past (Perfekt) is generally preferred in casual conversation, a few mixed verbs are very frequently used in their simple past (Präteritum) forms even in everyday speech. Verbs like rennen (rannte), bringen (brachte), and denken (dachte) are common in spoken German, particularly when recounting a story.

Why is it in den Schatten (accusative) here rather than im Schatten (dative)?

The preposition in is a two-way preposition. Because the perpetrator is moving from outside the shadow into the shadow (indicating direction towards a destination), we must use the accusative case (den Schatten). If he were already hiding and just running around within the shadow, you would use the dative (in dem Schatten or im Schatten).