A few points:

A) I don't believe it is possible to standby for international UA flights. Thus, you'll have to take your original IAD-FRA flight.

B) After the check-in agent issues you a departure management card (essentially a document that looks like a boarding pass and confirms your standby status), it is not strictly necessary to declare your standby intentions to the gate agent.

C) Getting on a DTW-FRA nonstop with Lufty is unlikely barring irregular operations or weather.

D) You are right in being worried about misconnecting from the evening DTW-IAD flight; late-day RJ operations are risky, as they tend to accumulate delays during the course of the day.

E) You will likely have to take a "moon-buggy" shuttle upon arrival at IAD from Terminal A to Term C, which can add up to 15 minutes to your transit time.

F) Consulting the seatmap for the earlier DTW-IAD flight is not the best way of assessing loads. Instead, go to www.seatcounter.com and enter the pertinent information regarding route and date (and also enter 'ua' twice into the favorite airline fields). This will provide you with real-time booking-class availability data. You should be particularly interested in the number of Y-booking-class tickets available, which should be an accurate gauge of the unsold seats on your flight (this assumes UA is not significantly overbooking your small RJ, which is a good assumption generally). Also, bear in mind that the largest number displayed for any booking class is 9. Thus, Y9 means there are 9 or more Y-booking-class seats available for sale.