All right, I'll try to answer... some things are related here.
Since the original delay was MX and it cascaded into your missing your connection, yes DL will cover the hotel. They normally provide vouchers in circumstances like this, but you can submit a complaint/feedback and briefly explain that a mechanical delay causes you to eventually miss your connection and have to overnight at DTW. They should end up sending you a check for the hotel. I'm assuming you had your bag so don't need to submit for incidentals like toothpaste etc.
Since you were on a paid first class fare and not a medallion upgrade, you should've been rebooked directly into F if there were any seats available, not put in Y and then on the upgrade list. In order to get irop priority for upgrade, it also has to be coded that way as a travel disruption. You should explain that you were on a first class fare and ask to be booked directly into first. This is assuming the flight was selling first... if not then the upgrade list as mentioned applies.
Also since you were downgraded from your original first class ticket, you are due compensation of $200 and the fare difference on your impacted segment(s) that you did not sit up front. I wonder if you've gotten this for your other MX issues this year and the meltdown.
Yes they keep track of complaints, however yours are not frivolous so should not be counted against you if thats what you're concerned about.