Upvote:7
The minimum connection time (MCT) at the Detroit airport for international to domestic connections is 1h30 (source), so with your 1h47 connection you should be fine. Note that for Delta-Delta connections (which is probably the case for you itinerary), the MCT is even lower, 1h20. Note also that immigration, customs, bag re-check, security, etc. are already factored into this minimum connection time.
Regarding your other questions: