Were UK landowners compensated for lands or homes taken by the British gov't during WWII? If so, what was the general rate per acre/home?

There is no single record source or comprehensive list of the land and properties that were requisitioned during conflict. Records of this nature were created by a range of different government departments, reflecting the interest many of them had in the requisitioning of land and property and in subsequent compensation payments. 

Yes we Lost Brookwood one of the worlds Famous Race tracks taken for the war effort and with Promises of being returned after WW2 but destroyed first By stupid Bureaucrats

Many Stately Homes destroyed by the Military who never cared about the Buildings the Americans destroyed farms with Concrete and everything that was British because they never cared

Yes.

Don't know.