Hello there mainebeachgurl !!
First of all, welcome to the forum. I hope you check out a lot of things using the search function as well as looking at the topics being discussed. After arriving here, please do stay in touch.
I'll put in what I feel to be the better way of thinking about some of the things you have asked about--remember, this is how I see it and can be mistaken to some degree in some areas.
Since you will be staying as a guest with a family, it may be better to perpare for a little more of a conservative attitude than usual--unless you have direct evidence saying the opposite.
I would say that while shorts would be o.k., 'short' shorts could make a little embarressment for some in the family--shorts are not that common.
I feel that a tank top would be o.k. as long as the material were not too thin. Cleavage? I don't see how that would be too much of a problem, but you might want to prepare for some looks.
Swimsuits are no sweat, any way you go, almost. You would probably notice when here, if you go swimming, that more girls your age than not wear swimsuits that are a little more than the typical bikini. You will probably appear older than the Japanese girl your age, however, so maybe whatever.
I guess the main thing you might want to keep in mind, is that you will be a guest at that family's house, and what you do will (most likely in their minds, at least) reflect on them. It would be different if you were totally on your own. 'Face' is important in Japan.
I hope you have fun here, and please do stay in touch. See you 'round !! MM