I subbed for Re:Zero, it's one of my favorite anime/web novels of all time. I vote for letting OPs/EDs play (when they do, this show often skips them in favor of making the episodes longer, like in this one).
1. One detail from these first few episodes is that the "Jealous Witch" is a slight mistranslation. It should be "Witch of Envy". The seven deadly sins motif is a big part of this show.
2. Elsa is THE Bowel Hunter, it's her nickname. (and bowels just revers to your guts in general)
3. Reinhard not using his sword wasn't actually his choice. His sword is the Dragon Sword Reid, and it can only be drawn against opponents that the sword deems worthy. That's why Reinhard said it was disappointing to him as well when he couldn't draw it.
4. This episode officially ends Arc 1: The Chaotic First Day. The first 4 arcs and 2 OVAs are animated so far, and here is the watch order:
Arc 1: The Chaotic First Day - Ep 1 - 3
Arc 2: The Tumultuous Week - Ep 4 - 11
OVA 1: Memory Snow
OVA 2: Frozen Bonds
Arc 3: The Return to the Capital City - Ep 12 - 25
Arc 4: The Everlasting Contract - All of Season 2
There are also 2 OVAs that need to be watched after Arc 2 (ep 11), they are Memory Snow and Frozen Bond
Sorry for the essay, but I'm always excited to see someone new jumping into this series, and I'll try to help with any questions you have!