my husband and I are going to Japan in May (Tokyo and Kyoto)
Avoid Golden Week in early May if you can. Other than that a very pleasant time to be in Japan (Tokyo and Kyoto).
Mont Fuji (day trip, no climbing): cruise on the lake to see the Mont Fuji and also the buddhist statues? Is it possible?
Possible. I'd pick either Five Lakes/Kawaguchiko or Hakone for the day trip.
Five Lakes is closer to the mountain and therefore you should have a bigger chance to see it. However there is not a whole lot to do (at least for my interests) besides watching Mount Fuji. Hakone is further from the mountain, but has a lot more to do besides it such as onsen, good museums, the old Tokaido road... As far as I am aware the cruise in Hakone is a lot more popular than the one in Five Lakes, probably also because it serves as a means of transport.
What Buddhist statues do you mean? Can only think of the Moto-Hakone Stone Buddhas at the moment. I liked these, but it is rather off-the beaten track.
how to get there from Tokyo, by train, by bus?
For Five Lakes, the easiest/cheapest is by direct bus, but you can also go there by train with one change.
For Hakone, many people chose to travel on a Hakone Free Pass which is a good deal if you do a bit of moving around in the Hakone area. In that case you'd travel by train on Odakyu Line up to Hakone-Yumoto which is basically the entrance point to the Hakone area. Inside the Hakone area you have all kinds of transport: buses, trains, ropeways, cablecars, boats...
I read in my French guide book that if we want to visit the Imperial Palace , we have to book tickets in advance by internet?
Which of the Imperial Palaces?
The one in Kyoto (which is a lot more interesting) can now be entered without a tour and without advance reservation.
The one in Tokyo (which is quite boring/modern) can only be entered with a tour which you can reserve through the Imperial Household Agency or get same-day registrations at the Kikyomon Gate of the palace.
do you know the name of the metro getting aroun Tokyo (a ring), to see the big city and rest a the same time?
Yamanote line
i am looking for a tea pot, round and quite flat, made of cast iron, for my mother? do you know where i can get this tea pot? and the prices
This can be anything from perhaps 2000 yen in a cheap department store or at Kappabashi Street for something made in China (?) up to many more yen for a handmade artist thing.
I would like to buy a necklace or ear rings with pearls from Japan. In Japan, the tax is 8 % and in France is 20 %, is it a good deal? cheaper than in France? the tax in Japan can be refund too?
No idea about this.