I've never heard of the difference between a "staked" and an "unstaked " survey. AFAIC, a survey must be staked. Otherwise, about all you have is a "courthouse survey" where the surveyor goes to the courthouse, looks up the plat, and copies it onto a drawing.
The surveyor should find or set a stake on every property corner. If a monument is found, it will not be reset unless the surveyor disagrees with it. In that case, he will set his own monumenty and describe both on the plat.
Each monument should be described on the plat and called out as "found" or "set." Usually, this is done with an abreviation. (e.g. FIP = Found Iron Pipe.) Is it possible that the surveyor found the monuments, which are something like pipes or rebars driven flush, and you can't find them again?
Around here, the surveyors usually set "Red Tops" next to each corner. A red top is a white painted wooden stake with a red painted top. They are not the corners, but are driven near the corners to make them easy to find. If you "own the street," they generally will not set monuments in the pavement.
As far as how far your property extends toward the street, that depends on the way the land was subdivided. In my current place, I own to the center of the street. Actually, to the centerline of the easement that allows the street. At my previous place, the Village owned the streets, which were on rights-of-way, not easements. I owned to one foot back of the sidewalk.
Talk with the surveyor. He should be able to explain his work.
