Does God Answer Prayers?

I stumbled upon an interesting post today, discussing whether God could respond to prayers and miraculously heal patients. The reasoning (which actually looks very pretty) was as follows:

Assumption (1). The patient currently has a medical problem.
Assumption (2). Praying for the patient to be healed can cause miraculous healing of that patient.
Assumption (3). The god to whom the prayer to heal the patient is directed :-

a) Exists;
b) Is all-powerful (omnipotent);
c) Is all-knowing (omniscient);
d) Has perfect judgement;
e) Will only do what is right;

Conclusion (4). An omnipotent being would be able to heal the patient (from 3a, 3b);
Conclusion (5). An omniscient being would already know about the patient’s problem. (from 1, 3a, 3c);
Conclusion (6). Any patient whom the god deems it right to heal will already be healed. (from 3d, 3e, 4, 5)
Conclusion (7). It is not right to heal the patient (from 1, 6).
Conclusion (8). Praying for the patient to heal will not cause miraculous healing of that patient (from 6, 7)

Contradiction : ( 2 & 8 )

Like I said, very pretty. But we can dismantle the argument very easily with another purely logical argument.

Imagine a god that is omnipotent. Would the god be able to create something that he could destroy? If so, he cannot destroy it, and therefore he is not omnipotent. If not, he cannot create it, and therefore he is not omnipotent.

The same thing applies to omniscience. Could this god be able to create a machine whose inner workings he cannot understand? If so, then he is not omniscient, because he cannot see the inner workings of the mechanism. If not, then he is not omniscient, because there exist a concept which he cannot create.

A god cannot, by logical definitions, be omnipotent or omniscient, therefore (ironically) conclusions 4 and 5 cannot hold by logical definitions. Thus, any subsequent conclusions drawn using conclusions 4 and 5 as a basis are falsified as well.

In essence, the argument disproves two radically opposing ideas - that a god can be omnipotent/omniscient, and that a god cannot heal through prayer.