Does searing cause more or less oil to be absorbed than frying?
Higher temperatures, as a rule, mean less absorption of oil because the force of the steam trying to escape from the food pushes against the oil.  Here is a link to a scholarly article discussing the mechanics of fat absorption in the production of french fries (complete with a table of results and diagrams).  Interestingly, the author says that potatoes deep fried at more than ten degrees Celsius below the recommended temperature of 180-185C leads to 40% higher fat uptake.  I expect pan-frying leads to a much lower total uptake of fat, but I am sure the principle is the same.

(For a fun explanation of the mechanics, here's Alton Brown in part II of the "Man Food" episode of Good Eats.  Enjoy.)

Now, your question was aimed at tofu (or some spongy equivalent), and you asked about the effects of flour vs no flour.  I could not find any articles with data on those exact elements of your question, but I suspect the answers will all derive from the same underlying principles.  In other words, as a rule, cooking at low or medium heat means that the spongy and/or dredged product will tend to absorb more fat than at high heat.

So, then, why do the recipes you have seen typically call for cooking tofu on "medium" heat?  My guess is that the recipe authors found that high heat makes the outside brown too much by the time the inside is "done" to the authors' preferences -- and perhaps a little extra oil in the tofu makes it taste better.  I am not sure, however, because most of the recipes I've seen call for searing a crust onto the tofu using medium-high heat.