Let me take a stab at the first question;
I think indeed you infer that statement. Your senses only provide you with entities. In order to arrive at the statement “the glass is on the table”, you have to relate those entities to the concepts of “glass”, “table”, and “being on” (i.e., inferring from the perceived characteristics of the entities to which concept they belong). As long as you accept the perceptual, and apply proper definitions, you can then indeed proceed to prove that the two entities you perceive are in fact a glass and a table, and than one is on the other, respectively.