For museums, I am not aware of a pass which is valid for entire Japan. There is a museum pass called Grutto Pass which is valid at 79 museums in Tokyo where admissions are discounted at each museum. Grutto Pass is not unlimited admission pass, although it is discounted you still pay admission at each museums. At what point (after how many museum visits) will Grutto Pass become economical, I do not know…

For trains, again there is no one pass which is valid for entire train system in Japan. Simple answer is because there are multiple train companies in Japan. What come closest is JR Rail Pass. There is a JR Rail Pass which is valid for entire JR lines in Japan. However, especially in large cities like Tokyo and Osaka there are subway lines and other commuter train companies where JR Rail pass is not valid. JR Rail Pass is unlimited ride pass. During the validity of JR Rail Pass (it comes in 7, 14 or 21 days) it is unlimited ride on JR lines. Also, JR Rail Pass is not valid on Nozomi bullet trains, which runs most frequently. JR Rail Pass is only valid on Hikari and Kodama bullet trains, which runs total of three per hour.