| a half wall is what id call a knee wall. usually comes up 4ft tall or so and is capped off with a 1x7 and maybe some trim around the bottom edge of the 1x7 to dress it up and cover the sheetrock edge.
if the wall is load bearing you are suposed to get a permit, ill leave it at that, would any one find out if you dont? i doubt it. people do this type stuff all the time with no permits.
the permits serve 2 purposes 1 makes sure you pay extra taxes, and 2 makes sure your not going to do something stupid and tear your house down.
as for a price on that, it all depends on how much your tearing out, as for a window or a see through, you want need a beam for this, but just a header is all. to span the distance of the window. now if you want a knee wall your looking at alot more money being that it involves removing a wall and installing a support beam either in the attic or just under the ceiling joist.
a budget for the window im guesses here maybe around $1500 +
that would cover removing the sheetrock and reframing the wall, mudding the sheetrock 3 coats and painting the wall. | 
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