Are goals from penalty shots counted into these two statistics?
(I mean penalty shots during the game, not in the shootout.)
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Penalty shots during regulation count toward the save percentage of the goalie (and toward the shooting percentage of the shooter). See for example:
Michael Frolik scored one of four Blackhawk goals on a penalty shot. He has a 1/2 Shooting % and Jimmy Howard has a 24/28 save statistic (not 24/27 as it would be if it didn't count) and 4 GA. You can also see that a penalty shot counts against the "Even Strength Goals Against", at least if it's not during a powerplay separately from the penalty that incurs the shot - Jimmy Howard has 3 EV GA and allowed one powerplay goal to open the scoring to Hossa.
Shootout goals do not count; for example:
Andrew Hammond has a 36/38 save statistic, for .947 sv%, despite allowing 3 goals during the shootout (out of 5 attempts).
No, they aren't. Only shots during regulation/overtime count, including penalty shots
Empt net goal also don't count, obviously, as the goalie isn't on the ice. Although every minute the goalie is off the ice affects his GAA as it isn't calculated by number of games played, but number of total minutes played divided by 60. If I goalie is only on the ice for 58 minutes it will slightly raise his GAA for the game. Likewise, playing overtime reduced the overal GAA as he would be playing more than 60 minutes.
So a goalie who lets in 3 goals in in a regulation game would have a GAA of 3.00 (assuming he plays every minute). A goalie who lets in 3 goals and gets pulled for the whole 3rd period would have a GAA of 4.55. Likewise a goalie who plays in a triple overtime game and allows 3 goals in 112 minutes when the winning goal is scored would have a GAA of 1.61