Yes it will physically fit. Check hasport for the mounts. They are weld on for the civic not sure about the teg. From the write ups I have seen the handling is only an issue if you are autocrossing it. Otherwise it is only a bit heavier and yes you will notice it in daily driving unless you corner like your grandma.
6 to 10 grand for just the swap? I don't think so but no it wont be as cheap as a B-series.
When talking chevies there is a simple rule that will also apply here. There is no substitute for cubic inches. You can build a small block chevy to have the horsepower of a big block chevy but it will drive like a race car while the big block still runs like a stocker. The more you have to build the less reliable the motor gets and the H-series is the big block of the Honda world. I puts out 200 horses reliably stock and you can build from there. To get 200 horses from the B-series you have to mod it and then it is not as reliable at those horses. Then to go beyond is obviously easier in the bigger motor that is starting at those levels.