Hey MJS,
Good idea to use your 241 on a trip to Tokyo. I did this earlier this year and is great value. Here's my answers to your questions:
1) March and April are good times to go, the weather begins to turn late may onwards. But for Cherry Blossom you need to go around the time your suggesting.
2) Seriously dont try and do Tokyo in less then a week - take your time there is so much to see and do. Perhaps break it up by spending the first part of the trip in Tokyo then go somewhere else (see point 3) and then return to Tokyo for a few days before travelling back to London (as your using 241 you will have to fly back from NRT anyway).
3) Kyoto is worth a trip (grab the Japan Rail card and taken the bullet train (shinkansen), I personally prefer Osaka to Kyoto (which is about 30 mins away by train).
4) Depends how much you want to spend, I stayed in the Park Hotel Tokyo which is part of the design group of hotels. Its located in Ginza and right next to the subway station, although its in Ginza it doesnt take long to travel anywhere else in Tokyo. The hotel takes the top 4 floors of the Shiodome Media Tower, apart from a really good rate, the room had amazing views of Tokyo including the Tokyo Tower.
5) No idea about doing a beach trip - didnt go in the right season
6) Be careful about availability in J to NRT, it used to be open all year round but this is becoming tighter and tighter. I had very fixed dates and had to travel out on the weekend, there was absolutely no availability in J for any weekend in 2008. So ended up doing F both ways. If you want to mix F and J, I would take F out to NRT (so you can take advantage of T5). In NRT you can check in earlier at a dedicated F desk (i arrived early as they were turning away other passengers on BA008 - however a flash of my F boarding card from OLCI meant i got pushed to the front). The lounge is owned by NWA and is a single lounge for both J and F so there's no advantage to flying F over J at NRT. However onboard you get a great selection of Japanese food in F on the way back - not sure what the J offering is.
Hope this helps
Chessy