Step in to TUCR and check out their Precision Noodle, I absolutely love mine for using small jigs and spoons. The rod will play anything that takes the bait, if you have 2-4lb test on a big pike will break the line before you have to worry about the rod breaking.
For #2 A lot of med-heavy ice rods will fit the bill. More important is the reel for that rod imo, I’ve seen James using some Okumas on his IFish Pros with a clicker that allows the reel to let line out freely with the bail closed, without messing with your drag.
#3 sounds to me like you may really like the Bullwhip or Quicktip at TUCR.
As for reels, I really like the Shimano Sedonas, I think I have 10-12 for ice fishing. There are a lot of reels I haven’t tried because I have been so content with these.
One thing I’ve learned with rods and reels for ice fishing is that you really get what you pay for. Up until about 4-5 years ago I went for the $29.99 combos at Joes, they let me down when I needed them most and I lost some good fish due to drags busting mid fight and rods breaking. Since then, my cheap rods are all fenwicks, my main rods are all TUCR (not that other custom rod guys don’t make a good stick, these guys have just always surpassed my expectations) and my reels are all Shimano.