Questions about trip to Japan for the first time

My wife and I are planning our first trip to Japan (April 2026 – 13 nights). We're treating it as an active, "honeymoon-style" trip (exploring, food, history).

We've booked open-jaw flights (Osaka in, Tokyo out) and have done some research. Our draft plan follows the 'Golden Route': Osaka -> Kyoto (with Nara) -> Hakone -> Tokyo.

We have a few questions. We would greatly appreciate your advice before making a reservation.

Our Main Questions:
LUGGAGE: Can we take our suitcases with us on the Shinkansen when changing cities? If so, is there an extra charge?

ACCOMMODATION (Airbnb vs. Hotel): We are currently planning to use Airbnbs for most of the trip to save money. Is this a good idea for a first trip?

PACING & ROUTE (The 2-4-2-5 Split): Our current draft allocates our 13 nights as: 2 (Osaka) + 4 (Kyoto) + 2 (Hakone) + 5 (Tokyo). Does this sound like a balanced pace, or is it still too rushed? We're wondering if we should skip a stop (like Osaka or Hakone) to have more "deep dive" time in just Kyoto and Tokyo.

JR PASS: For this specific route (Osaka -> Kyoto -> Odawara [for Hakone] -> Tokyo), our math suggests a national JR Pass is not worth it, and we should just buy point-to-point Shinkansen tickets. Does this sound correct?

SHOPPING LOCATIONS: Our shopping goals are specific: Tech, Watches, and Streetwear/Sneakers. We've mapped out Harajuku/Shibuya for streetwear (Atmos, Ura-Harajuku) and Akihabara or Nakano Broadway for tech/watches. Are these the right areas, or are we missing better spots?

Thank you for your help!

by TopVoice6369