I would like to live on a house boat. I have these romantic notions about it but don't know if it is realistic. Do you know anything about Houseboats?
Yes, I actually own an lives in a houseboat, which is primarily my home.
Is it safe and how big do they get?
Yes its safe, if its kept stationary at a fixed point. As big as you can afford it!
When were houseboats first built, how long have they been around? 
Houseboats have been built around since the late 1950s/early 1960s
Thats a  while back but don't know if its long enough of a time period to workout all the faults that may occur. I would actually like my houseboat to be able to be a form of transportation. Do you know if there is such a house boat?
Yes, in Western countries, houseboats tend to be also used for transport!