Think 3 and 4

Think 3 : Though the temperature of both the tile and the parquet is the same,our sense of touch is a poor estimate of temperature,thus the tile feels colder.Both the parquet and tile has a lower temperature than our legs and so we lose thermal energy to them,but since we lose thermal energy to the tile at a faster rate than the parquet,it feels colder.

Think 4 :  The hotter water will lose thermal energy to the colder water, the colder water will gain heat from the colder water.After a while, they will reach the same temperature.(temperature equilibrium).