In an episode of TNG, Q gave Riker God-like powers. Aside from this incident, did the Q ever give/lend their powers to mortal beings? If one receives the powers, would he be considered a Q?
Technically in TNG: Deja Q, Q starts off as a mortal human. He was stripped of his powers and given a choice to be turned into anything, so he chose human.
Now, I realize that Q wasn't born human, and that he used to be a Q, and--setting aside questions about the "reality" of a Q's actions and creations--the following does fit within the confines of your question as asked: when the Q continuum made Q (the mortal) a Q (albeit again), they granted powers to a mortal.
I know this is not the example you are looking for. But the mortal-Q was truly just a human. Then he was a Q (again).
They can, and they did. In the episode Hide and Q Q bestows Riker with Q powers. Aside from Riker there are no canon (i.e. TV or movie) examples of a mortal being given the Q power, although it is possible to be born with them.
As to that mortal then being considered Q, anyone with the Q powers is Q (the Continuum considered Amanda Rogers to be Q, even though she was born and raised as a human). But it is possible to give up the powers (or have them taken away) and thus become a mortal (again).
Arguably the Q, in allowing the crew of the Voyager to enter the Q Continuum and operate Q weaponry in VOY: The Q and the Grey shared some of their powers.
FEMALE Q: Q and I have a plan to end the war. Call off your troops.
JANEWAY: Do as she says and I'll call my people off.
FEMALE Q: They may be humanoids, but they're using our weapons.
COLONEL Q: Cease fire! Cease fire!