When a player shoots the cue ball but does not make contact with any other ball nor with any cushion on purpose e.g. like a safety shot, I know that is not a legal shot in eight ball. Does the opponent get ball-in-hand or ball-in-kitchen? What if the cue ball makes no it makes no contact with any ball but does hit a cushion? Is that a legal shot? If a player did this while shooting at the 8 ball as their last ball, would that be loss of game for that player?
When a player uses the 8 ball in a combination shot to pocket their own ball, does the opponent get ball-in-kitchen or is it just his turn to shoot?
In 8 Ball billiards, when you fault, as in the safety play that you described, the opponent would have "ball-in-hand." (according to BCA) Note that this is one of the most disagreed-upon rules in 8-ball pool. If you are playing in a league, or in a bar, be sure to confirm this before playing. If only hitting rails, and no object ball, the shot is NOT legal. For the third part of your first question, the answer is yes, it would result in loss of game, according to BCA.
Once all the player's object balls are pocketed, he/she can now attempt to sink the 8 ball and win. To win, he/she must specify the pocket it will land in, and make it in that pocket. If it is shot in to the wrong pocket, if the cue ball is potted, or if there is a fault (see below), he/she loses. If neither the cue ball nor the eight ball is potted, the player's inning is over.