Air Interception has a range corresponding to the normal range of the unit I think - maybe a little less? Anyway, it has a range, and if an enemy airplane tries to target on of your units or cities that is within this range, your air unit will attack the enem plane damaging them (but also taking damage itself) whereas the original target will go unharmed. Each airplane can only intercept once per turn unless you have the Sortie upgrade.
Air Sweeping an AA unit will do a tiny bit of damage to your airplane I think, something like 3-5 points of damage (out of 100). It will use up the intercept attack of the AA gun for that turn. If there are multiple AA guns, you'll need to do multiple Air Sweeps. If there are intercepting enemy airplanes, they'll engage with your fighter preventing the Air Sweep as per a normal Interception if I'm not mistaken. If you Air Sweep an area and there are no AA guns or defending Fighters within the region your Fighter will not suffer damage but will use it's turn and you get a message that it encountered no resistance.