1) You're completely right about the first meaning. I'm going to go ahead and assume (from Lauren's answer) that in American English the second meaning is rarely used.
2) In British English you can use "halfway house" to refer to a stopping place on a journey. This could be a hotel or inn. eg. "It'll take us two days to get up there, so we'll use the Shangri La hotel as our halfway house".
3) FURTHERMORE, you can use this term metaphorically. It just means a "stopping point" between two ideas or concepts.
For instance, "Following the end of the war, a provisional government was set up. This was just a halfway house between the civil war, which had raged for 5 years, and the modern government we see today". = The halfway house is the provisional government ... it was just temporary solution between the civil war and the modern government.
"Middle English was used for hundreds of years but it was only ever a halfway house between the now almost incomprehensible Old English and the modern English that we all speak today." = Middle English was just a stopping point (even for a few hundred years!) in the progression of the language into what it has become today.
By the way, "Middle English" refers to the English that was written/spoken in the times of Chaucer (1300s), which is before Shakespeare (1500s) but after the time when "Old English" (600 AD - 1100 AD) was written/spoken. Middle English is difficult but possible to understand for a native speaker with some practice [you'd want a dictionary nearby! Well, I did anyway!]. Old English is almost like another language and requires extensive practice and study to understand.
A Google search reveals a "halfway house" to be "the halfway point in a progression". That is the point that I have been trying to convey.
Does this make sense to you? If you want any more explanation just post a comment and I will have another go. This one is quite difficult to describe (its metaphorical use, I mean).