Since the surveyor's plat gets updated with the easement, it's part of the due diligence while the property is in escrow. When I bought my new home last year, I had the sidewalk easement spelled out in mind-numbing detail by the escrow agent when I signed the closing papers.
Does the easement remain part of the property until the time it is to be taken?
Generally, once the easement is sold, the easement goes into effect immediately, and anything on that easement is now at risk.
Does the deed have to show that the new owners purchased a land with an easement on it that could be exercised while they hold the property?
Yes.
There could have been a crooked deal, the deed might not have declared the easement since it was done in 1960 who knows?
Trust me, they knew about easements and recording them in 1960, even in poor, benighted South Carolina. My house was build in 1966, and the easement for the sidewalk was spelled out to within an inch of the easement's life. Since the state owned the easement, it was undoubtedly recorded on the surveyor's plat filed at the county assessor's office.