My flight lands in NRT early afternoon, next flight departs from HND around midnight, have 10 hours in between. Was thinking about stopping by Shinjuku for a few hours on the way.

1. Goal is to eat at a place I like in Kabukicho. Maybe get Hokkaido milk bun at a Mont Thabor.
2. I plan to take NEX to Shinjuku, and Haneda Limousine Bus to HND from Busta Shinjuku. The NEX arrival point and HND bus departure point are very close to each other, is that right?
3. I would get a Welcome Suica upon landing in NRT, which I believe works on both NEX and the HND bus. I understand the minimum amount to load is 1000 yen, I'd load a bit more to cover the transportation.
4. Do I need to reserve the HND bus, say, upon landing in NRT, or just tap my Welcome Suica card when boarding bus?
5. I have 4 pieces of luggage. Plan is to store those in a locker or something near Shinjuku station, then pick up in a few hours. Any suggestions and how much $$ would it cost?
6. I see temperature tomorrow is around 100F with possible rain, neither fun for walking around (esp if need to store luggage outdoor). Would you stick to this plan, or just go straight to HND and spend more time in the lounge? (I'm flying ANA J)

Thanks.